NPB Model for Birth Weight
Sheena Martenies
02/10/2021
#' -----------------------------------------------------------------------------
#' Install the new version of the package
#' -----------------------------------------------------------------------------
#library(devtools)
#install_github("lvhoskovec/mmpack", build_vignettes = TRUE, force = TRUE)
library(tidyverse)## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.0 ──## ✓ ggplot2 3.3.3 ✓ purrr 0.3.4
## ✓ tibble 3.0.6 ✓ dplyr 1.0.4
## ✓ tidyr 1.1.2 ✓ stringr 1.4.0
## ✓ readr 1.3.1 ✓ forcats 0.5.0## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()library(lubridate)##
## Attaching package: 'lubridate'## The following objects are masked from 'package:base':
##
## date, intersect, setdiff, unionlibrary(haven)
library(readxl)
library(mmpack)
#' For ggplots
simple_theme <- theme(
#aspect.ratio = 1,
text = element_text(family="Calibri",size = 12, color = 'black'),
panel.spacing.y = unit(0,"cm"),
panel.spacing.x = unit(0.25, "lines"),
panel.grid.minor = element_line(color = "transparent"),
panel.grid.major = element_line(color = "transparent"),
panel.border=element_rect(fill = NA),
panel.background=element_blank(),
axis.ticks = element_line(colour = "black"),
axis.text = element_text(color = "black", size=10),
# legend.position = c(0.1,0.1),
plot.margin=grid::unit(c(0,0,0,0), "mm"),
legend.key = element_blank()
)
# windowsFonts(Calibri=windowsFont("TT Calibri"))
options(scipen = 9999) #avoid scientific notation
set.seed(123)1 Sensitivty Analysis
In this version of the analysis, we are excluding race/ethnicity because the DAG may indicate the race/ethnicty are on the causal path (modifers, not confounders)
1.1 Exposure data
#' Exposure data
X <- select(hs_data2, mean_pm, mean_o3, mean_temp, pct_tree_cover, pct_impervious,
mean_aadt_intensity, dist_m_tri:dist_m_mine_well,
cvd_rate_adj, res_rate_adj, violent_crime_rate, property_crime_rate,
pct_less_hs, pct_unemp, pct_limited_eng, pct_hh_pov, pct_poc) %>%
as.matrix()
head(X)## mean_pm mean_o3 mean_temp pct_tree_cover pct_impervious
## [1,] 8.483046 47.19072 51.81487 6.006276 43.30893
## [2,] 6.598608 50.05090 58.32885 7.281109 48.36432
## [3,] 7.454146 48.57052 58.01924 17.205991 31.67281
## [4,] 6.671239 50.06429 61.35590 6.842898 45.00359
## [5,] 7.122537 50.14275 59.28421 3.357792 28.16745
## [6,] 7.637453 47.03125 55.32825 10.743612 45.87564
## mean_aadt_intensity dist_m_tri dist_m_npl dist_m_waste_site
## [1,] 10128.4962 2827.538 729.2371 4829.780
## [2,] 10749.0359 1576.420 5239.2211 4417.792
## [3,] 9048.6468 3350.303 2992.2968 5211.871
## [4,] 4223.3434 3364.954 6998.1286 8921.318
## [5,] 858.7283 2923.811 3427.2247 7006.042
## [6,] 15603.9800 3364.200 3166.5395 4484.960
## dist_m_major_emit dist_m_cafo dist_m_mine_well cvd_rate_adj res_rate_adj
## [1,] 7968.654 29116.58 1749.1256 275.2480 155.7767
## [2,] 3780.951 51044.30 7354.5310 279.6435 226.8038
## [3,] 7423.232 36079.21 4887.2996 221.0414 157.6974
## [4,] 9636.816 42235.78 3752.6399 203.8812 142.5368
## [5,] 6806.912 29145.98 729.7784 194.1983 101.0046
## [6,] 5265.285 43921.85 5870.6867 174.3361 120.3281
## violent_crime_rate property_crime_rate pct_less_hs pct_unemp
## [1,] 14.377133 37.32935 31.784946 11.529628
## [2,] 8.905404 67.03932 15.290231 4.908306
## [3,] 7.636888 46.78194 6.891702 4.564963
## [4,] 2.850212 21.95270 2.725915 5.623583
## [5,] 5.435988 22.49834 12.919186 5.234103
## [6,] 5.035971 47.15500 3.842365 10.000000
## pct_limited_eng pct_hh_pov pct_poc
## [1,] 26.114650 12.010919 90.33703
## [2,] 8.500401 18.123496 30.44025
## [3,] 0.000000 6.307978 26.63305
## [4,] 1.350621 9.292274 32.68648
## [5,] 6.307385 2.115768 73.60772
## [6,] 5.121799 25.171768 23.08698Variance and histograms of the exposure variables (in their original units):
var(X)## mean_pm mean_o3 mean_temp pct_tree_cover
## mean_pm 0.391784015 0.006083605 0.09741867 -0.2054297
## mean_o3 0.006083605 9.383489039 11.72688428 -0.4158151
## mean_temp 0.097418667 11.726884276 20.59970005 0.4425544
## pct_tree_cover -0.205429726 -0.415815089 0.44255440 9.7193077
## pct_impervious 0.508898445 -1.674151031 3.35723856 5.8719893
## mean_aadt_intensity -182.234953786 474.627052967 2674.12174077 8431.6446632
## dist_m_tri -255.176839682 444.286548683 -627.63132786 -73.1423054
## dist_m_npl -289.002141382 539.849185829 -165.00509261 434.4654007
## dist_m_waste_site -275.262105884 261.902915064 58.19389166 1933.8647304
## dist_m_major_emit 71.096593638 577.257325397 138.98687089 265.4284518
## dist_m_cafo -1291.237441927 -35.275020052 237.89751842 10170.6234275
## dist_m_mine_well -339.250592215 -375.434990683 -202.34883778 3136.3680766
## cvd_rate_adj 3.871688575 0.939328342 7.31791796 -24.8232924
## res_rate_adj 2.356328835 -0.181515705 7.98167422 -3.5331376
## violent_crime_rate 0.232839920 0.577648302 1.07794996 -4.0583754
## property_crime_rate 2.001989749 -2.773092354 6.06649992 -22.6429724
## pct_less_hs 1.132232861 0.637361326 0.69410116 -7.5753471
## pct_unemp 0.100439902 0.288530482 0.25729682 -0.3330523
## pct_limited_eng 0.432516169 0.295617023 0.05811301 -2.8349116
## pct_hh_pov 0.731824476 -0.606648513 0.73475917 0.3805472
## pct_poc 1.632059580 1.202932299 -0.90133106 -19.4091792
## pct_impervious mean_aadt_intensity dist_m_tri
## mean_pm 0.5088984 -182.2350 -255.17684
## mean_o3 -1.6741510 474.6271 444.28655
## mean_temp 3.3572386 2674.1217 -627.63133
## pct_tree_cover 5.8719893 8431.6447 -73.14231
## pct_impervious 176.8316214 55459.6063 -15279.44024
## mean_aadt_intensity 55459.6063235 67283287.0201 -1315386.69307
## dist_m_tri -15279.4402428 -1315386.6931 6558190.20296
## dist_m_npl -7729.3843793 1683196.0799 4282727.94125
## dist_m_waste_site -4662.9983638 2039577.9230 2441267.84540
## dist_m_major_emit 2627.0270993 2477155.3406 1433153.16531
## dist_m_cafo 16586.9964129 15462371.9832 3431065.70215
## dist_m_mine_well 706.6674650 2073244.5987 995872.11873
## cvd_rate_adj 230.4542985 20477.4374 -49347.60273
## res_rate_adj 176.8108084 33055.3733 -31870.98664
## violent_crime_rate 26.6945028 5736.5627 -1014.08753
## property_crime_rate 118.0737725 22077.3894 -5365.69285
## pct_less_hs 56.8383947 -4056.6889 -12372.14262
## pct_unemp 25.9434246 6003.3343 -2527.22451
## pct_limited_eng 41.9919053 2620.6198 -5408.86434
## pct_hh_pov 82.2198624 17850.1649 -8842.76408
## pct_poc 88.3560154 4526.2710 -18049.42332
## dist_m_npl dist_m_waste_site dist_m_major_emit
## mean_pm -289.0021 -275.26211 71.09659
## mean_o3 539.8492 261.90292 577.25733
## mean_temp -165.0051 58.19389 138.98687
## pct_tree_cover 434.4654 1933.86473 265.42845
## pct_impervious -7729.3844 -4662.99836 2627.02710
## mean_aadt_intensity 1683196.0799 2039577.92299 2477155.34057
## dist_m_tri 4282727.9413 2441267.84540 1433153.16531
## dist_m_npl 11125411.7474 4193498.05859 6948817.25739
## dist_m_waste_site 4193498.0586 5344101.75397 1395277.06805
## dist_m_major_emit 6948817.2574 1395277.06805 10114549.72263
## dist_m_cafo 5416531.1320 5586018.82514 -2993791.05377
## dist_m_mine_well 256924.3029 1375784.78556 -1810174.74785
## cvd_rate_adj -30921.0390 -43119.57852 16272.40152
## res_rate_adj -19393.1304 -32402.84395 -1320.21297
## violent_crime_rate -672.9264 -3702.61118 -360.49700
## property_crime_rate -18283.4264 -22350.30055 -24007.42305
## pct_less_hs -6760.5337 -11422.49855 8866.74917
## pct_unemp 2195.0515 -1476.40942 5212.74830
## pct_limited_eng 498.0033 -4277.81339 9367.28435
## pct_hh_pov -1135.3843 -7599.74324 8682.26135
## pct_poc -1456.8941 -8602.85207 22698.24353
## dist_m_cafo dist_m_mine_well cvd_rate_adj
## mean_pm -1291.23744 -339.2506 3.8716886
## mean_o3 -35.27502 -375.4350 0.9393283
## mean_temp 237.89752 -202.3488 7.3179180
## pct_tree_cover 10170.62343 3136.3681 -24.8232924
## pct_impervious 16586.99641 706.6675 230.4542985
## mean_aadt_intensity 15462371.98316 2073244.5987 20477.4373759
## dist_m_tri 3431065.70215 995872.1187 -49347.6027339
## dist_m_npl 5416531.13199 256924.3029 -30921.0389720
## dist_m_waste_site 5586018.82514 1375784.7856 -43119.5785165
## dist_m_major_emit -2993791.05377 -1810174.7478 16272.4015197
## dist_m_cafo 46324000.89481 9345575.3772 -46645.9665229
## dist_m_mine_well 9345575.37722 4430024.9964 -39046.5984701
## cvd_rate_adj -46645.96652 -39046.5985 2039.8569530
## res_rate_adj -13772.40263 -16322.5110 1289.5661935
## violent_crime_rate 722.31907 -2032.3464 135.9487143
## property_crime_rate -15833.92381 -4272.3829 343.9364726
## pct_less_hs -26060.83378 -10037.6577 328.3044447
## pct_unemp -1030.96916 -2827.2369 105.0153846
## pct_limited_eng -7089.15821 -4814.6687 183.5853966
## pct_hh_pov -855.38016 -5030.4055 266.1004715
## pct_poc -44526.37107 -24974.3303 618.2817294
## res_rate_adj violent_crime_rate property_crime_rate
## mean_pm 2.3563288 0.2328399 2.001990
## mean_o3 -0.1815157 0.5776483 -2.773092
## mean_temp 7.9816742 1.0779500 6.066500
## pct_tree_cover -3.5331376 -4.0583754 -22.642972
## pct_impervious 176.8108084 26.6945028 118.073773
## mean_aadt_intensity 33055.3733277 5736.5627383 22077.389365
## dist_m_tri -31870.9866403 -1014.0875345 -5365.692846
## dist_m_npl -19393.1304345 -672.9263612 -18283.426420
## dist_m_waste_site -32402.8439544 -3702.6111771 -22350.300554
## dist_m_major_emit -1320.2129699 -360.4970006 -24007.423046
## dist_m_cafo -13772.4026269 722.3190727 -15833.923813
## dist_m_mine_well -16322.5110008 -2032.3464340 -4272.382880
## cvd_rate_adj 1289.5661935 135.9487143 343.936473
## res_rate_adj 1091.1856742 104.4979610 333.780710
## violent_crime_rate 104.4979610 40.1175363 160.725724
## property_crime_rate 333.7807097 160.7257236 1295.004010
## pct_less_hs 197.8827546 22.5579950 -3.138375
## pct_unemp 72.3576933 11.3130282 1.362247
## pct_limited_eng 104.0524036 12.7978322 -14.963510
## pct_hh_pov 201.6582659 29.1947400 64.236239
## pct_poc 297.8399442 46.4013012 -44.321973
## pct_less_hs pct_unemp pct_limited_eng pct_hh_pov
## mean_pm 1.1322329 0.1004399 0.43251617 0.7318245
## mean_o3 0.6373613 0.2885305 0.29561702 -0.6066485
## mean_temp 0.6941012 0.2572968 0.05811301 0.7347592
## pct_tree_cover -7.5753471 -0.3330523 -2.83491161 0.3805472
## pct_impervious 56.8383947 25.9434246 41.99190527 82.2198624
## mean_aadt_intensity -4056.6889048 6003.3343312 2620.61975287 17850.1649192
## dist_m_tri -12372.1426191 -2527.2245090 -5408.86433682 -8842.7640785
## dist_m_npl -6760.5337115 2195.0514738 498.00334199 -1135.3843390
## dist_m_waste_site -11422.4985495 -1476.4094188 -4277.81339346 -7599.7432386
## dist_m_major_emit 8866.7491706 5212.7483023 9367.28434718 8682.2613524
## dist_m_cafo -26060.8337755 -1030.9691591 -7089.15821141 -855.3801591
## dist_m_mine_well -10037.6576614 -2827.2368665 -4814.66874000 -5030.4055237
## cvd_rate_adj 328.3044447 105.0153846 183.58539661 266.1004715
## res_rate_adj 197.8827546 72.3576933 104.05240356 201.6582659
## violent_crime_rate 22.5579950 11.3130282 12.79783224 29.1947400
## property_crime_rate -3.1383751 1.3622468 -14.96351049 64.2362387
## pct_less_hs 162.1681017 39.4206217 85.19100137 100.9072175
## pct_unemp 39.4206217 24.6546969 25.21727694 36.9693212
## pct_limited_eng 85.1910014 25.2172769 68.65329426 67.2758215
## pct_hh_pov 100.9072175 36.9693212 67.27582153 119.7157808
## pct_poc 238.8801445 72.7999599 142.19618383 155.4992975
## pct_poc
## mean_pm 1.6320596
## mean_o3 1.2029323
## mean_temp -0.9013311
## pct_tree_cover -19.4091792
## pct_impervious 88.3560154
## mean_aadt_intensity 4526.2710457
## dist_m_tri -18049.4233248
## dist_m_npl -1456.8941447
## dist_m_waste_site -8602.8520680
## dist_m_major_emit 22698.2435288
## dist_m_cafo -44526.3710716
## dist_m_mine_well -24974.3303024
## cvd_rate_adj 618.2817294
## res_rate_adj 297.8399442
## violent_crime_rate 46.4013012
## property_crime_rate -44.3219731
## pct_less_hs 238.8801445
## pct_unemp 72.7999599
## pct_limited_eng 142.1961838
## pct_hh_pov 155.4992975
## pct_poc 524.7591044ggplot(pivot_longer(as.data.frame(X), mean_pm:pct_poc, names_to = "exp", values_to = "value")) +
geom_histogram(aes(x = value)) +
facet_wrap(~ exp, scales = "free")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Scaling the exposure variables
X.scaled <- apply(X, 2, scale)
head(X.scaled)## mean_pm mean_o3 mean_temp pct_tree_cover pct_impervious
## [1,] 1.60876944 -0.2502907 -0.1690421 -0.08261827 0.2084897
## [2,] -1.40186806 0.6834152 1.2661699 0.32629926 0.5886571
## [3,] -0.03503482 0.2001460 1.1979551 3.50981981 -0.6665506
## [4,] -1.28583023 0.6877893 1.9331141 0.18573791 0.3359288
## [5,] -0.56482237 0.7133998 1.4766616 -0.93215008 -0.9301550
## [6,] 0.25782234 -0.3023500 0.6050531 1.43693690 0.4015075
## mean_aadt_intensity dist_m_tri dist_m_npl dist_m_waste_site
## [1,] -0.02626143 -0.4008664 -1.44212141 -0.172775897
## [2,] 0.04938980 -0.8894134 -0.08999604 -0.350992130
## [3,] -0.15790801 -0.1967327 -0.76363997 -0.007492447
## [4,] -0.74617032 -0.1910117 0.43733697 1.597126043
## [5,] -1.15635722 -0.3632728 -0.63324550 0.768623456
## [6,] 0.64126566 -0.1913062 -0.71140077 -0.321936759
## dist_m_major_emit dist_m_cafo dist_m_mine_well cvd_rate_adj res_rate_adj
## [1,] -0.1090638 -1.1354079 -0.7748959 0.6917151 -0.2847192
## [2,] -1.4258114 2.0863310 1.8883051 0.7890362 1.8654606
## [3,] -0.2805619 -0.1124210 0.7160914 -0.5084805 -0.2265752
## [4,] 0.4154599 0.7921355 0.1769998 -0.8884275 -0.6855261
## [5,] -0.4743524 -1.1310891 -1.2592010 -1.1028189 -1.9428184
## [6,] -0.9590895 1.0398621 1.1833114 -1.5425892 -1.3578439
## violent_crime_rate property_crime_rate pct_less_hs pct_unemp
## [1,] 0.2444833 -0.5008789 1.20091488 0.36793456
## [2,] -0.6194047 0.3247153 -0.09436047 -0.96557105
## [3,] -0.8196807 -0.2382061 -0.75386917 -1.03471894
## [4,] -1.5754111 -0.9281724 -1.08099463 -0.82151747
## [5,] -1.1671633 -0.9130100 -0.28055077 -0.89995692
## [6,] -1.2303189 -0.2278392 -0.99332353 0.05987409
## pct_limited_eng pct_hh_pov pct_poc
## [1,] 2.15383825 -0.3020187 1.5727240
## [2,] 0.02798425 0.2566428 -1.0419857
## [3,] -0.99792447 -0.8232412 -1.2081839
## [4,] -0.83491873 -0.5504902 -0.9439299
## [5,] -0.23668961 -1.2063898 0.8424295
## [6,] -0.37977738 0.9008223 -1.3629822Variance and histograms of the exposure variables (scaled):
var(X.scaled)## mean_pm mean_o3 mean_temp pct_tree_cover
## mean_pm 1.000000000 0.003172893 0.034291650 -0.105274276
## mean_o3 0.003172893 1.000000000 0.843470729 -0.043541201
## mean_temp 0.034291650 0.843470729 1.000000000 0.031276529
## pct_tree_cover -0.105274276 -0.043541201 0.031276529 1.000000000
## pct_impervious 0.061140333 -0.041099117 0.055625226 0.141640558
## mean_aadt_intensity -0.035493982 0.018889337 0.071828554 0.329716765
## dist_m_tri -0.159193706 0.056635532 -0.053998558 -0.009161339
## dist_m_npl -0.138426634 0.052836279 -0.010899557 0.041781063
## dist_m_waste_site -0.190232937 0.036984589 0.005546380 0.268331135
## dist_m_major_emit 0.035715124 0.059253499 0.009628753 0.026770503
## dist_m_cafo -0.303095664 -0.001691929 0.007701165 0.479321466
## dist_m_mine_well -0.257510042 -0.058230361 -0.021182010 0.477976199
## cvd_rate_adj 0.136954783 0.006789463 0.035699097 -0.176295758
## res_rate_adj 0.113962827 -0.001793836 0.053237079 -0.034307854
## violent_crime_rate 0.058730941 0.029772424 0.037497389 -0.205526308
## property_crime_rate 0.088879773 -0.025156291 0.037142591 -0.201827442
## pct_less_hs 0.142046220 0.016338825 0.012009076 -0.190810449
## pct_unemp 0.032317153 0.018969666 0.011417056 -0.021515177
## pct_limited_eng 0.083396591 0.011647067 0.001545298 -0.109746623
## pct_hh_pov 0.106858205 -0.018100029 0.014795814 0.011156172
## pct_poc 0.113823690 0.017142692 -0.008669098 -0.271775006
## pct_impervious mean_aadt_intensity dist_m_tri dist_m_npl
## mean_pm 0.06114033 -0.03549398 -0.159193706 -0.13842663
## mean_o3 -0.04109912 0.01888934 0.056635532 0.05283628
## mean_temp 0.05562523 0.07182855 -0.053998558 -0.01089956
## pct_tree_cover 0.14164056 0.32971677 -0.009161339 0.04178106
## pct_impervious 1.00000000 0.50844411 -0.448678724 -0.17426369
## mean_aadt_intensity 0.50844411 1.00000000 -0.062619247 0.06152095
## dist_m_tri -0.44867872 -0.06261925 1.000000000 0.50138396
## dist_m_npl -0.17426369 0.06152095 0.501383960 1.00000000
## dist_m_waste_site -0.15168685 0.10755964 0.412369055 0.54385239
## dist_m_major_emit 0.06211712 0.09495686 0.175965418 0.65505772
## dist_m_cafo 0.18326720 0.27696155 0.196849357 0.23859436
## dist_m_mine_well 0.02524829 0.12008641 0.184760224 0.03659688
## cvd_rate_adj 0.38371166 0.05527416 -0.426652406 -0.20525615
## res_rate_adj 0.40251263 0.12199419 -0.376750794 -0.17601130
## violent_crime_rate 0.31693831 0.11041575 -0.062519618 -0.03185242
## property_crime_rate 0.24673907 0.07479259 -0.058223492 -0.15232247
## pct_less_hs 0.33564418 -0.03883608 -0.379376300 -0.15916230
## pct_unemp 0.39291400 0.14739715 -0.198747643 0.13253691
## pct_limited_eng 0.38111402 0.03855846 -0.254907958 0.01801953
## pct_hh_pov 0.56509450 0.19888999 -0.315587892 -0.03111065
## pct_poc 0.29005220 0.02408835 -0.307674381 -0.01906733
## dist_m_waste_site dist_m_major_emit dist_m_cafo
## mean_pm -0.19023294 0.035715124 -0.303095664
## mean_o3 0.03698459 0.059253499 -0.001691929
## mean_temp 0.00554638 0.009628753 0.007701165
## pct_tree_cover 0.26833114 0.026770503 0.479321466
## pct_impervious -0.15168685 0.062117120 0.183267205
## mean_aadt_intensity 0.10755964 0.094956864 0.276961553
## dist_m_tri 0.41236906 0.175965418 0.196849357
## dist_m_npl 0.54385239 0.655057717 0.238594356
## dist_m_waste_site 1.00000000 0.189779728 0.355027509
## dist_m_major_emit 0.18977973 1.000000000 -0.138307324
## dist_m_cafo 0.35502751 -0.138307324 1.000000000
## dist_m_mine_well 0.28275484 -0.270423318 0.652378929
## cvd_rate_adj -0.41298787 0.113286594 -0.151743889
## res_rate_adj -0.42432287 -0.012566704 -0.061257230
## violent_crime_rate -0.25287368 -0.017896218 0.016755559
## property_crime_rate -0.26866460 -0.209766780 -0.064647236
## pct_less_hs -0.38800832 0.218931589 -0.300678627
## pct_unemp -0.12862329 0.330098571 -0.030506530
## pct_limited_eng -0.22333346 0.355475551 -0.125707430
## pct_hh_pov -0.30045944 0.249507656 -0.011486308
## pct_poc -0.16245202 0.311558055 -0.285584268
## dist_m_mine_well cvd_rate_adj res_rate_adj
## mean_pm -0.25751004 0.136954783 0.113962827
## mean_o3 -0.05823036 0.006789463 -0.001793836
## mean_temp -0.02118201 0.035699097 0.053237079
## pct_tree_cover 0.47797620 -0.176295758 -0.034307854
## pct_impervious 0.02524829 0.383711656 0.402512635
## mean_aadt_intensity 0.12008641 0.055274160 0.121994187
## dist_m_tri 0.18476022 -0.426652406 -0.376750794
## dist_m_npl 0.03659688 -0.205256148 -0.176011297
## dist_m_waste_site 0.28275484 -0.412987865 -0.424322872
## dist_m_major_emit -0.27042332 0.113286594 -0.012566704
## dist_m_cafo 0.65237893 -0.151743889 -0.061257230
## dist_m_mine_well 1.00000000 -0.410752544 -0.234765650
## cvd_rate_adj -0.41075254 1.000000000 0.864359590
## res_rate_adj -0.23476565 0.864359590 1.000000000
## violent_crime_rate -0.15245003 0.475234675 0.499449246
## property_crime_rate -0.05640681 0.211613232 0.280786581
## pct_less_hs -0.37449548 0.570813439 0.470409304
## pct_unemp -0.27052616 0.468277441 0.441149256
## pct_limited_eng -0.27607853 0.490577454 0.380164971
## pct_hh_pov -0.21843600 0.538480631 0.557944498
## pct_poc -0.51797735 0.597594464 0.393598671
## violent_crime_rate property_crime_rate pct_less_hs
## mean_pm 0.05873094 0.088879773 0.14204622
## mean_o3 0.02977242 -0.025156291 0.01633882
## mean_temp 0.03749739 0.037142591 0.01200908
## pct_tree_cover -0.20552631 -0.201827442 -0.19081045
## pct_impervious 0.31693831 0.246739067 0.33564418
## mean_aadt_intensity 0.11041575 0.074792588 -0.03883608
## dist_m_tri -0.06251962 -0.058223492 -0.37937630
## dist_m_npl -0.03185242 -0.152322474 -0.15916230
## dist_m_waste_site -0.25287368 -0.268664603 -0.38800832
## dist_m_major_emit -0.01789622 -0.209766780 0.21893159
## dist_m_cafo 0.01675556 -0.064647236 -0.30067863
## dist_m_mine_well -0.15245003 -0.056406808 -0.37449548
## cvd_rate_adj 0.47523468 0.211613232 0.57081344
## res_rate_adj 0.49944925 0.280786581 0.47040930
## violent_crime_rate 1.00000000 0.705151942 0.27967307
## property_crime_rate 0.70515194 1.000000000 -0.00684836
## pct_less_hs 0.27967307 -0.006848360 1.00000000
## pct_unemp 0.35971778 0.007623781 0.62343462
## pct_limited_eng 0.24385889 -0.050184228 0.80738433
## pct_hh_pov 0.42127121 0.163143151 0.72420883
## pct_poc 0.31980337 -0.053765481 0.81887450
## pct_unemp pct_limited_eng pct_hh_pov pct_poc
## mean_pm 0.032317153 0.083396591 0.10685820 0.113823690
## mean_o3 0.018969666 0.011647067 -0.01810003 0.017142692
## mean_temp 0.011417056 0.001545298 0.01479581 -0.008669098
## pct_tree_cover -0.021515177 -0.109746623 0.01115617 -0.271775006
## pct_impervious 0.392914001 0.381114020 0.56509450 0.290052202
## mean_aadt_intensity 0.147397153 0.038558463 0.19888999 0.024088345
## dist_m_tri -0.198747643 -0.254907958 -0.31558789 -0.307674381
## dist_m_npl 0.132536906 0.018019533 -0.03111065 -0.019067333
## dist_m_waste_site -0.128623290 -0.223333456 -0.30045944 -0.162452016
## dist_m_major_emit 0.330098571 0.355475551 0.24950766 0.311558055
## dist_m_cafo -0.030506530 -0.125707430 -0.01148631 -0.285584268
## dist_m_mine_well -0.270526163 -0.276078529 -0.21843600 -0.517977353
## cvd_rate_adj 0.468277441 0.490577454 0.53848063 0.597594464
## res_rate_adj 0.441149256 0.380164971 0.55794450 0.393598671
## violent_crime_rate 0.359717785 0.243858891 0.42127121 0.319803374
## property_crime_rate 0.007623781 -0.050184228 0.16314315 -0.053765481
## pct_less_hs 0.623434625 0.807384330 0.72420883 0.818874497
## pct_unemp 1.000000000 0.612939575 0.68048090 0.640031449
## pct_limited_eng 0.612939575 1.000000000 0.74208323 0.749164620
## pct_hh_pov 0.680480902 0.742083231 1.00000000 0.620401357
## pct_poc 0.640031449 0.749164620 0.62040136 1.000000000ggplot(pivot_longer(as.data.frame(X.scaled), mean_pm:pct_poc,
names_to = "exp", values_to = "value")) +
geom_histogram(aes(x = value)) +
facet_wrap(~ exp, scales = "free")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
1.2 Covariate data
Covariates were assessed at the individual level. These were selected based on previous HS studies and others in the literature and informed by a DAG.
W <- select(hs_data2,
lat, lon, lat_lon_int,
ed_no_hs, ed_hs, ed_aa, ed_4yr,
low_bmi, ovwt_bmi, obese_bmi,
concep_spring, concep_summer, concep_fall,
concep_2010, concep_2011, concep_2012, concep_2013,
maternal_age, any_smoker, smokeSH, mean_cpss, mean_epsd,
male, gest_age_w) %>%
as.matrix()
head(W)## lat lon lat_lon_int ed_no_hs ed_hs ed_aa ed_4yr low_bmi
## [1,] 39.79402 -104.8133 -4170.944 0 0 1 0 0
## [2,] 39.62671 -104.9927 -4160.517 0 0 1 0 0
## [3,] 39.74934 -104.9129 -4170.219 0 0 0 0 0
## [4,] 39.68397 -104.8933 -4162.583 0 0 1 0 0
## [5,] 39.79134 -104.7669 -4168.814 0 0 0 1 0
## [6,] 39.68050 -104.9451 -4164.274 0 0 1 0 0
## ovwt_bmi obese_bmi concep_spring concep_summer concep_fall concep_2010
## [1,] 0 0 0 0 0 0
## [2,] 0 0 0 0 0 1
## [3,] 0 0 0 0 0 1
## [4,] 0 0 1 0 0 1
## [5,] 0 0 1 0 0 1
## [6,] 0 0 0 0 0 1
## concep_2011 concep_2012 concep_2013 maternal_age any_smoker smokeSH
## [1,] 0 0 0 19 0 1
## [2,] 0 0 0 36 0 0
## [3,] 0 0 0 34 0 0
## [4,] 0 0 0 28 0 0
## [5,] 0 0 0 30 0 0
## [6,] 0 0 0 22 0 0
## mean_cpss mean_epsd male gest_age_w
## [1,] 29 0 0 40.57143
## [2,] 19 2 1 35.85714
## [3,] 19 1 0 40.42857
## [4,] 20 0 0 36.28571
## [5,] 15 0 1 38.42857
## [6,] 17 1 0 40.71429Scaled the non-binary (continuous) covariates
colnames(W)## [1] "lat" "lon" "lat_lon_int" "ed_no_hs"
## [5] "ed_hs" "ed_aa" "ed_4yr" "low_bmi"
## [9] "ovwt_bmi" "obese_bmi" "concep_spring" "concep_summer"
## [13] "concep_fall" "concep_2010" "concep_2011" "concep_2012"
## [17] "concep_2013" "maternal_age" "any_smoker" "smokeSH"
## [21] "mean_cpss" "mean_epsd" "male" "gest_age_w"W.s <- apply(W[,c(1, 2, 3, 18, 21, 22, 24)], 2, scale) #' just the continuous ones
W.scaled <- cbind(W.s[,1:3],
W[,4:17], W.s[,4],
W[,19:20], W.s[,5:6],
W[,23], W.s[,7])
colnames(W.scaled)## [1] "lat" "lon" "lat_lon_int" "ed_no_hs"
## [5] "ed_hs" "ed_aa" "ed_4yr" "low_bmi"
## [9] "ovwt_bmi" "obese_bmi" "concep_spring" "concep_summer"
## [13] "concep_fall" "concep_2010" "concep_2011" "concep_2012"
## [17] "concep_2013" "" "any_smoker" "smokeSH"
## [21] "mean_cpss" "mean_epsd" "" ""colnames(W.scaled) <- colnames(W)
head(W.scaled)## lat lon lat_lon_int ed_no_hs ed_hs ed_aa ed_4yr low_bmi
## [1,] 0.9587536 0.5410850 -0.5821980 0 0 1 0 0
## [2,] -1.5498523 -1.6236392 0.6519093 0 0 1 0 0
## [3,] 0.2887793 -0.6606299 -0.4964164 0 0 0 0 0
## [4,] -0.6913627 -0.4239607 0.4073829 0 0 1 0 0
## [5,] 0.9185421 1.1019032 -0.3300513 0 0 0 1 0
## [6,] -0.7433125 -1.0489343 0.2071583 0 0 1 0 0
## ovwt_bmi obese_bmi concep_spring concep_summer concep_fall concep_2010
## [1,] 0 0 0 0 0 0
## [2,] 0 0 0 0 0 1
## [3,] 0 0 0 0 0 1
## [4,] 0 0 1 0 0 1
## [5,] 0 0 1 0 0 1
## [6,] 0 0 0 0 0 1
## concep_2011 concep_2012 concep_2013 maternal_age any_smoker smokeSH
## [1,] 0 0 0 -1.39815187 0 1
## [2,] 0 0 0 1.35109608 0 0
## [3,] 0 0 0 1.02765515 0 0
## [4,] 0 0 0 0.05733234 0 0
## [5,] 0 0 0 0.38077328 0 0
## [6,] 0 0 0 -0.91299047 0 0
## mean_cpss mean_epsd male gest_age_w
## [1,] 3.3147856 -1.2832098 0 0.7037686
## [2,] 0.1179652 -0.6860171 1 -1.9146645
## [3,] 0.1179652 -0.9846134 0 0.6244221
## [4,] 0.4376472 -1.2832098 0 -1.6766251
## [5,] -1.1607630 -1.2832098 1 -0.4864283
## [6,] -0.5213989 -0.9846134 0 0.7831150summary(W.scaled)## lat lon lat_lon_int ed_no_hs
## Min. :-2.45418 Min. :-2.5043 Min. :-3.48430 Min. :0.0000
## 1st Qu.:-0.62577 1st Qu.:-0.5848 1st Qu.:-0.48738 1st Qu.:0.0000
## Median : 0.03151 Median : 0.1214 Median : 0.02121 Median :0.0000
## Mean : 0.00000 Mean : 0.0000 Mean : 0.00000 Mean :0.1527
## 3rd Qu.: 0.42402 3rd Qu.: 0.6654 3rd Qu.: 0.60627 3rd Qu.:0.0000
## Max. : 4.00304 Max. : 4.5531 Max. : 2.60273 Max. :1.0000
## ed_hs ed_aa ed_4yr low_bmi
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.00000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.00000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.00000
## Mean :0.1851 Mean :0.2319 Mean :0.2185 Mean :0.03344
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.00000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.00000
## ovwt_bmi obese_bmi concep_spring concep_summer
## Min. :0.000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.262 Mean :0.1996 Mean :0.2497 Mean :0.2408
## 3rd Qu.:1.000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## concep_fall concep_2010 concep_2011 concep_2012
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.2709 Mean :0.1616 Mean :0.3021 Mean :0.2932
## 3rd Qu.:1.0000 3rd Qu.:0.0000 3rd Qu.:1.0000 3rd Qu.:1.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## concep_2013 maternal_age any_smoker smokeSH
## Min. :0.0000 Min. :-1.88331 Min. :0.00000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:-0.91299 1st Qu.:0.00000 1st Qu.:0.0000
## Median :0.0000 Median : 0.05733 Median :0.00000 Median :0.0000
## Mean :0.2419 Mean : 0.00000 Mean :0.08696 Mean :0.2575
## 3rd Qu.:0.0000 3rd Qu.: 0.70421 3rd Qu.:0.00000 3rd Qu.:1.0000
## Max. :1.0000 Max. : 2.64486 Max. :1.00000 Max. :1.0000
## mean_cpss mean_epsd male gest_age_w
## Min. :-5.9560 Min. :-1.2832 Min. :0.0000 Min. :-7.7070
## 1st Qu.:-0.5214 1st Qu.:-0.7855 1st Qu.:0.0000 1st Qu.:-0.3277
## Median : 0.0114 Median :-0.1884 Median :1.0000 Median : 0.1483
## Mean : 0.0000 Mean : 0.0000 Mean :0.5117 Mean : 0.0000
## 3rd Qu.: 0.5442 3rd Qu.: 0.6079 3rd Qu.:1.0000 3rd Qu.: 0.6244
## Max. : 4.5935 Max. : 6.0324 Max. :1.0000 Max. : 2.9255Variance and histograms for the scaled covariates
var(W.scaled)## lat lon lat_lon_int ed_no_hs
## lat 1.000000000 -0.25261855699 -0.926170284 0.0058668471
## lon -0.252618557 1.00000000000 0.598841550 0.0173291290
## lat_lon_int -0.926170284 0.59884155012 1.000000000 0.0019047436
## ed_no_hs 0.005866847 0.01732912905 0.001904744 0.1295488931
## ed_hs -0.013065279 0.04117136599 0.026869409 -0.0282962056
## ed_aa -0.007178943 0.04676104709 0.024182422 -0.0354554865
## ed_4yr 0.002235236 -0.00766878563 -0.004860779 -0.0334099777
## low_bmi -0.002977458 -0.00003551643 0.002453115 -0.0039977007
## ovwt_bmi 0.020588007 0.00512460048 -0.015060264 0.0045849757
## obese_bmi 0.016566934 0.00976713009 -0.009896473 0.0063181836
## concep_spring 0.014329290 -0.00046075172 -0.012039363 -0.0002364031
## concep_summer -0.014031905 -0.00711327850 0.008844405 -0.0044530877
## concep_fall 0.005490559 0.01642183233 0.001845775 0.0110338032
## concep_2010 0.011068124 0.00844610317 -0.005886105 -0.0001629937
## concep_2011 -0.022063544 0.01869831001 0.025541096 0.0096091635
## concep_2012 0.002443596 -0.00706763788 -0.004770794 -0.0035360925
## concep_2013 0.007481786 -0.02068066481 -0.014234422 -0.0057396182
## maternal_age 0.030778940 -0.17980907079 -0.095594562 -0.1376124653
## any_smoker -0.008227433 0.02279799333 0.015696371 0.0179541925
## smokeSH -0.011104226 0.04668855425 0.027384613 0.0309364548
## mean_cpss -0.025836085 -0.01114736129 0.017046231 -0.0561153540
## mean_epsd -0.034737548 0.05084465609 0.048585549 0.0670107276
## male 0.029004763 -0.02552947737 -0.033951919 -0.0135085702
## gest_age_w 0.011119160 -0.03926647196 -0.024532454 -0.0076928484
## ed_hs ed_aa ed_4yr low_bmi
## lat -0.01306527915 -0.007178943 0.0022352364 -0.00297745845
## lon 0.04117136599 0.046761047 -0.0076687856 -0.00003551643
## lat_lon_int 0.02686940852 0.024182422 -0.0048607788 0.00245311454
## ed_no_hs -0.02829620561 -0.035455487 -0.0334099777 -0.00399770067
## ed_hs 0.15098194378 -0.042960663 -0.0404821628 -0.00173196369
## ed_aa -0.04296066253 0.178312629 -0.0507246377 0.00786102484
## ed_4yr -0.04048216276 -0.050724638 0.1709517837 -0.00173569637
## low_bmi -0.00173196369 0.007861025 -0.0017356964 0.03236233875
## ovwt_bmi -0.00612657270 0.015075052 0.0040748427 -0.00877179885
## obese_bmi 0.02441297380 0.009478520 -0.0124024526 -0.00668149785
## concep_spring 0.00395788541 0.006761128 -0.0066354615 -0.00501298973
## concep_summer -0.00331835284 -0.011257764 0.0064762004 0.00309812470
## concep_fall 0.00226573698 -0.007084627 0.0010078237 0.00320637243
## concep_2010 0.00576574693 0.004884834 0.0003533604 0.00128404204
## concep_2011 -0.00463350056 0.002410067 0.0053402214 0.00439336479
## concep_2012 0.00371526119 -0.005564182 -0.0061016882 -0.00535266364
## concep_2013 -0.00464096592 -0.002587992 0.0006519748 -0.00028741639
## maternal_age -0.10868310364 -0.040296710 0.1091044519 -0.01089529356
## any_smoker 0.00174689441 0.011063665 -0.0156735248 0.00155279503
## smokeSH 0.02483352246 0.022806677 -0.0362443263 0.00142215122
## mean_cpss -0.03433895561 0.030714793 0.0282429323 0.00484169668
## mean_epsd 0.02014619096 0.025424770 -0.0463684315 0.00946748435
## male 0.00006345557 0.000630823 0.0063679527 -0.00262407430
## gest_age_w -0.01723767893 -0.035168407 0.0301476493 -0.00601412877
## ovwt_bmi obese_bmi concep_spring concep_summer
## lat 0.0205880066 0.0165669344 0.0143292896 -0.01403190526
## lon 0.0051246005 0.0097671301 -0.0004607517 -0.00711327850
## lat_lon_int -0.0150602639 -0.0098964732 -0.0120393632 0.00884440451
## ed_no_hs 0.0045849757 0.0063181836 -0.0002364031 -0.00445308767
## ed_hs -0.0061265727 0.0244129738 0.0039578854 -0.00331835284
## ed_aa 0.0150750518 0.0094785197 0.0067611284 -0.01125776398
## ed_4yr 0.0040748427 -0.0124024526 -0.0066354615 0.00647620043
## low_bmi -0.0087717989 -0.0066814978 -0.0050129897 0.00309812470
## ovwt_bmi 0.1935643614 -0.0523383998 0.0092806876 -0.00512123746
## obese_bmi -0.0523383998 0.1599105152 -0.0085938744 -0.00346392738
## concep_spring 0.0092806876 -0.0085938744 0.1875696767 -0.06020066890
## concep_summer -0.0051212375 -0.0034639274 -0.0602006689 0.18302078356
## concep_fall 0.0026091436 0.0005673674 -0.0677257525 -0.06530697563
## concep_2010 -0.0033345278 -0.0043921206 -0.0236714146 0.00009331701
## concep_2011 0.0055828456 0.0032598742 0.0003633142 -0.00140348782
## concep_2012 -0.0043547938 0.0072737498 -0.0085677457 0.00186260750
## concep_2013 0.0023988692 -0.0059187868 0.0321545529 -0.00028368371
## maternal_age 0.0089002276 0.0027900741 -0.0149065532 0.01490413862
## any_smoker -0.0060656056 0.0027173913 0.0016983696 0.00024262422
## smokeSH -0.0106232083 0.0110524666 -0.0041134138 -0.00627836837
## mean_cpss -0.0082476896 -0.0087226114 0.0079650833 0.01166899615
## mean_epsd -0.0019127169 0.0281330380 -0.0063209443 -0.01563660013
## male 0.0008361204 -0.0017804885 -0.0062746357 -0.00393797778
## gest_age_w -0.0148466585 -0.0214614301 -0.0179961830 0.01920131892
## concep_fall concep_2010 concep_2011 concep_2012
## lat 0.0054905592 0.01106812411 -0.0220635440 0.002443596
## lon 0.0164218323 0.00844610317 0.0186983100 -0.007067638
## lat_lon_int 0.0018457750 -0.00588610547 0.0255410960 -0.004770794
## ed_no_hs 0.0110338032 -0.00016299371 0.0096091635 -0.003536093
## ed_hs 0.0022657370 0.00576574693 -0.0046335006 0.003715261
## ed_aa -0.0070846273 0.00488483437 0.0024100673 -0.005564182
## ed_4yr 0.0010078237 0.00035336041 0.0053402214 -0.006101688
## low_bmi 0.0032063724 0.00128404204 0.0043933648 -0.005352664
## ovwt_bmi 0.0026091436 -0.00333452779 0.0055828456 -0.004354794
## obese_bmi 0.0005673674 -0.00439212056 0.0032598742 0.007273750
## concep_spring -0.0677257525 -0.02367141464 0.0003633142 -0.008567746
## concep_summer -0.0653069756 0.00009331701 -0.0014034878 0.001862608
## concep_fall 0.1977350096 0.02870431199 -0.0127396381 0.001955925
## concep_2010 0.0287043120 0.13567048893 -0.0488918916 -0.047448589
## concep_2011 -0.0127396381 -0.04889189162 0.2110780976 -0.088679776
## concep_2012 0.0019559245 -0.04744858855 -0.0886797758 0.207464863
## concep_2013 -0.0176182513 -0.03914959588 -0.0731692447 -0.071009267
## maternal_age -0.0196470231 -0.02663971411 -0.0380704459 0.031448396
## any_smoker -0.0023777174 0.00266886646 0.0105298913 -0.011015140
## smokeSH -0.0028778966 0.00631569517 0.0136280160 -0.018670867
## mean_cpss -0.0055888831 0.00832724099 -0.0113573536 -0.011161856
## mean_epsd 0.0265650931 -0.01748485806 0.0347867417 -0.022850868
## male 0.0018476768 0.00089584329 -0.0029824116 -0.001761825
## gest_age_w 0.0141959621 0.01072301448 -0.0118973482 -0.026416733
## concep_2013 maternal_age any_smoker smokeSH
## lat 0.0074817863 0.030778940 -0.0082274331 -0.011104226
## lon -0.0206806648 -0.179809071 0.0227979933 0.046688554
## lat_lon_int -0.0142344221 -0.095594562 0.0156963705 0.027384613
## ed_no_hs -0.0057396182 -0.137612465 0.0179541925 0.030936455
## ed_hs -0.0046409659 -0.108683104 0.0017468944 0.024833522
## ed_aa -0.0025879917 -0.040296710 0.0110636646 0.022806677
## ed_4yr 0.0006519748 0.109104452 -0.0156735248 -0.036244326
## low_bmi -0.0002874164 -0.010895294 0.0015527950 0.001422151
## ovwt_bmi 0.0023988692 0.008900228 -0.0060656056 -0.010623208
## obese_bmi -0.0059187868 0.002790074 0.0027173913 0.011052467
## concep_spring 0.0321545529 -0.014906553 0.0016983696 -0.004113414
## concep_summer -0.0002836837 0.014904139 0.0002426242 -0.006278368
## concep_fall -0.0176182513 -0.019647023 -0.0023777174 -0.002877897
## concep_2010 -0.0391495959 -0.026639714 0.0026688665 0.006315695
## concep_2011 -0.0731692447 -0.038070446 0.0105298913 0.013628016
## concep_2012 -0.0710092670 0.031448396 -0.0110151398 -0.018670867
## concep_2013 0.1835981048 0.034822201 -0.0020865683 -0.002101499
## maternal_age 0.0348222009 1.000000000 -0.0466296108 -0.155964054
## any_smoker -0.0020865683 -0.046629611 0.0794836957 0.049010093
## smokeSH -0.0021014990 -0.155964054 0.0490100932 0.191419314
## mean_cpss 0.0104924310 0.100637638 0.0176429080 0.031721118
## mean_epsd 0.0069811381 -0.160410684 0.0421446647 0.108180210
## male 0.0044194935 0.023413804 0.0023291925 0.002004449
## gest_age_w 0.0268056111 0.091663607 -0.0149814181 -0.050311537
## mean_cpss mean_epsd male gest_age_w
## lat -0.025836085 -0.034737548 0.02900476291 0.011119160
## lon -0.011147361 0.050844656 -0.02552947737 -0.039266472
## lat_lon_int 0.017046231 0.048585549 -0.03395191918 -0.024532454
## ed_no_hs -0.056115354 0.067010728 -0.01350857023 -0.007692848
## ed_hs -0.034338956 0.020146191 0.00006345557 -0.017237679
## ed_aa 0.030714793 0.025424770 0.00063082298 -0.035168407
## ed_4yr 0.028242932 -0.046368432 0.00636795270 0.030147649
## low_bmi 0.004841697 0.009467484 -0.00262407430 -0.006014129
## ovwt_bmi -0.008247690 -0.001912717 0.00083612040 -0.014846658
## obese_bmi -0.008722611 0.028133038 -0.00178048853 -0.021461430
## concep_spring 0.007965083 -0.006320944 -0.00627463569 -0.017996183
## concep_summer 0.011668996 -0.015636600 -0.00393797778 0.019201319
## concep_fall -0.005588883 0.026565093 0.00184767678 0.014195962
## concep_2010 0.008327241 -0.017484858 0.00089584329 0.010723014
## concep_2011 -0.011357354 0.034786742 -0.00298241161 -0.011897348
## concep_2012 -0.011161856 -0.022850868 -0.00176182513 -0.026416733
## concep_2013 0.010492431 0.006981138 0.00441949355 0.026805611
## maternal_age 0.100637638 -0.160410684 0.02341380415 0.091663607
## any_smoker 0.017642908 0.042144665 0.00232919255 -0.014981418
## smokeSH 0.031721118 0.108180210 0.00200444935 -0.050311537
## mean_cpss 1.000000000 0.455187203 -0.00331530432 -0.037142336
## mean_epsd 0.455187203 1.000000000 0.00154181454 -0.137187808
## male -0.003315304 0.001541815 0.25014184185 -0.007427180
## gest_age_w -0.037142336 -0.137187808 -0.00742717951 1.000000000ggplot(pivot_longer(as.data.frame(W.scaled), lat:gest_age_w,
names_to = "exp", values_to = "value")) +
geom_histogram(aes(x = value)) +
facet_wrap(~ exp, scales = "free")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
1.3 Response data: birth weight (in grams)
Y <- select(hs_data2, birth_weight) %>%
as.matrix()
head(Y)## birth_weight
## [1,] 2860
## [2,] 2755
## [3,] 3505
## [4,] 2695
## [5,] 3355
## [6,] 3810Distribution of birth weight and scaled birth weight
hist(Y, breaks = 20)
hist(scale(Y), breaks = 20)
Dropping gest_age_w from the covariates
colnames(W.scaled)## [1] "lat" "lon" "lat_lon_int" "ed_no_hs"
## [5] "ed_hs" "ed_aa" "ed_4yr" "low_bmi"
## [9] "ovwt_bmi" "obese_bmi" "concep_spring" "concep_summer"
## [13] "concep_fall" "concep_2010" "concep_2011" "concep_2012"
## [17] "concep_2013" "maternal_age" "any_smoker" "smokeSH"
## [21] "mean_cpss" "mean_epsd" "male" "gest_age_w"W.scaled2 <- W.scaled[,-c(ncol(W.scaled))]
colnames(W.scaled2)## [1] "lat" "lon" "lat_lon_int" "ed_no_hs"
## [5] "ed_hs" "ed_aa" "ed_4yr" "low_bmi"
## [9] "ovwt_bmi" "obese_bmi" "concep_spring" "concep_summer"
## [13] "concep_fall" "concep_2010" "concep_2011" "concep_2012"
## [17] "concep_2013" "maternal_age" "any_smoker" "smokeSH"
## [21] "mean_cpss" "mean_epsd" "male"2 RIDGE regression
To see if there might be something going on, Lauren suggested a ridge regression with a small penalty.
set.seed(123)
library(glmnet)## Loading required package: Matrix##
## Attaching package: 'Matrix'## The following objects are masked from 'package:tidyr':
##
## expand, pack, unpack## Loaded glmnet 4.0-2lambda_seq <- 10^seq(4, -4, by = -.05)
#' Best lambda from CV
ridge_cv <- cv.glmnet(X, Y, alpha = 0, lambda = lambda_seq,
standardize = T, standardize.response = T)
plot(ridge_cv)
best_lambda <- ridge_cv$lambda.min
best_lambda## [1] 891.2509#' Fit the model using the best_lambda
bw_ridge <- glmnet(X, Y, alpha = 0, lambda = best_lambda,
standardize = T, standardize.response = T)
summary(bw_ridge)## Length Class Mode
## a0 1 -none- numeric
## beta 21 dgCMatrix S4
## df 1 -none- numeric
## dim 2 -none- numeric
## lambda 1 -none- numeric
## dev.ratio 1 -none- numeric
## nulldev 1 -none- numeric
## npasses 1 -none- numeric
## jerr 1 -none- numeric
## offset 1 -none- logical
## call 7 -none- call
## nobs 1 -none- numericRidge regression coefficients
coef(bw_ridge)## 22 x 1 sparse Matrix of class "dgCMatrix"
## s0
## (Intercept) 3756.2244127611
## mean_pm 6.5831658736
## mean_o3 -5.7909309972
## mean_temp -2.6190406717
## pct_tree_cover 0.0346391254
## pct_impervious -0.4281346032
## mean_aadt_intensity -0.0002915500
## dist_m_tri -0.0003520682
## dist_m_npl 0.0001168135
## dist_m_waste_site 0.0017447014
## dist_m_major_emit -0.0003705192
## dist_m_cafo -0.0003121004
## dist_m_mine_well -0.0022906005
## cvd_rate_adj -0.1469368176
## res_rate_adj -0.1446242346
## violent_crime_rate -0.4156388202
## property_crime_rate -0.0143345439
## pct_less_hs -0.6736508410
## pct_unemp -3.6551596165
## pct_limited_eng -0.5218862220
## pct_hh_pov -0.4758794734
## pct_poc -0.4466466437Ridge regression predictions
ridge_pred <- predict(bw_ridge, newx = X)
plot(Y, ridge_pred)
actual <- Y
preds <- ridge_pred
rsq <- 1 - (sum((preds - actual) ^ 2))/(sum((actual - mean(actual)) ^ 2))The R2 value for this model is 0.03. Based on these results, it doesn’t look like there’s much here.
3 Nonparametric Bayesian Shrinkage (NPB): Birth weight
3.1 Finding the NPB priors
3.1.1 Vignette Priors
set.seed(123)
priors.npb.1 <- list(alpha.pi = 1, beta.pi = 1, alpha.pi2 = 9, beta.pi2 = 1,
a.phi1 = 1)
fit.npb.1 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
scaleY = TRUE,
priors = priors.npb.1, interact = F)
npb.sum.1 <- summary(fit.npb.1)
npb.sum.1$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] -0.05907077 1.7292064 0.000000 0 0.008
## [2,] -1.18173936 6.7453018 -22.846654 0 0.050
## [3,] -0.68874315 5.1022188 -3.829552 0 0.032
## [4,] -0.09836726 1.3523591 0.000000 0 0.014
## [5,] -0.58334088 4.2590450 -2.025017 0 0.028
## [6,] -0.02810779 1.3627030 0.000000 0 0.018
## [7,] -0.07241864 1.6862869 0.000000 0 0.010
## [8,] 0.12843949 1.6692407 0.000000 0 0.016
## [9,] 0.29614136 3.3791200 0.000000 0 0.020
## [10,] -0.04574610 1.1661326 0.000000 0 0.010
## [11,] -1.02549044 12.1015196 -21.361864 0 0.048
## [12,] -0.76889738 5.1972449 -7.703709 0 0.032
## [13,] -0.50082159 4.2854699 -1.645144 0 0.028
## [14,] -0.52647452 4.1378266 0.000000 0 0.020
## [15,] -0.14443889 1.7466026 0.000000 0 0.018
## [16,] -0.03206135 0.8482502 0.000000 0 0.012
## [17,] -0.71146302 4.8104069 -9.104986 0 0.032
## [18,] -6.57484938 17.6038554 -65.994065 0 0.150
## [19,] -0.32089031 3.4509916 0.000000 0 0.016
## [20,] -0.21027072 2.1926996 0.000000 0 0.016
## [21,] -0.63622272 5.4262819 0.000000 0 0.026plot(fit.npb.1$beta[,1], type = "l")
plot(fit.npb.1$beta[,2], type = "l")
plot(fit.npb.1$beta[,13], type = "l")
3.1.2 Try making a.phi1 = 10 and sig2inv.mu1 = 10
priors.npb.24 <- list(alpha.pi = 5, beta.pi = 5, alpha.pi2 = 9, beta.pi2 = 1,
a.phi1 = 10, sig2inv.mu1 = 10)
fit.npb.24 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
scaleY = TRUE,
priors = priors.npb.24, interact = F)
npb.sum.24 <- summary(fit.npb.24)
npb.sum.24$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] -0.37835158 6.444211 -12.39843 15.459027 0.254
## [2,] -6.50866456 13.285146 -47.61147 5.157978 0.422
## [3,] -2.99829637 9.530987 -27.10395 9.170820 0.316
## [4,] -1.83469729 7.302263 -20.66994 8.664141 0.302
## [5,] -4.15010395 8.878299 -31.18568 1.432763 0.364
## [6,] -1.13456265 5.999765 -13.20965 9.648707 0.262
## [7,] -1.06393850 6.067273 -14.88747 10.146850 0.274
## [8,] -0.41269500 6.179682 -13.50993 11.850908 0.238
## [9,] 0.08388743 7.009746 -12.23644 21.113180 0.262
## [10,] -0.45998103 6.272873 -11.69475 11.850908 0.238
## [11,] -2.86724980 11.352373 -33.00612 8.125983 0.348
## [12,] -3.68104712 8.584663 -26.86129 3.369650 0.354
## [13,] -3.81491402 8.769486 -30.58368 3.211650 0.382
## [14,] -3.48433858 7.905814 -25.16353 3.591160 0.354
## [15,] -1.13941047 5.331153 -14.58868 4.475193 0.232
## [16,] -2.06055760 6.610397 -19.45050 7.383645 0.310
## [17,] -2.67440654 7.648666 -25.96178 7.642657 0.336
## [18,] -17.54869944 23.031327 -74.98278 0.000000 0.664
## [19,] -2.39876713 6.867868 -19.15311 7.383645 0.338
## [20,] -2.19811559 7.659921 -22.28194 8.860543 0.332
## [21,] -2.38098284 7.546698 -22.00851 9.174345 0.372plot(fit.npb.24$beta[,1], type = "l")
plot(fit.npb.24$beta[,2], type = "l")
plot(fit.npb.24$beta[,13], type = "l")
3.2 Fit the NPB model without temperature
Below I’ve used the set of priors labeled “24” and set scaleY = T
The priors are as follows: r priors.npb.24
Note that this version of the model does not include gest_age_w. It does include an indicator variable for season of conception (ref = winter) and the lon/lat as covariates and the percentage of the census tract population that is not NHW as an exposure.
priors.npb <- priors.npb.24
#' Exposures (minus temperature)
colnames(X.scaled)## [1] "mean_pm" "mean_o3" "mean_temp"
## [4] "pct_tree_cover" "pct_impervious" "mean_aadt_intensity"
## [7] "dist_m_tri" "dist_m_npl" "dist_m_waste_site"
## [10] "dist_m_major_emit" "dist_m_cafo" "dist_m_mine_well"
## [13] "cvd_rate_adj" "res_rate_adj" "violent_crime_rate"
## [16] "property_crime_rate" "pct_less_hs" "pct_unemp"
## [19] "pct_limited_eng" "pct_hh_pov" "pct_poc"#' Covariates
colnames(W.scaled2)## [1] "lat" "lon" "lat_lon_int" "ed_no_hs"
## [5] "ed_hs" "ed_aa" "ed_4yr" "low_bmi"
## [9] "ovwt_bmi" "obese_bmi" "concep_spring" "concep_summer"
## [13] "concep_fall" "concep_2010" "concep_2011" "concep_2012"
## [17] "concep_2013" "maternal_age" "any_smoker" "smokeSH"
## [21] "mean_cpss" "mean_epsd" "male"# fit.npb <- npb(niter = 5000, nburn = 2500, X = X.scaled[,-c(3)], Y = Y, W = W.scaled2,
# scaleY = TRUE,
# priors = priors.npb, interact = TRUE, XWinteract = TRUE)
# save(fit.npb, file = here::here("Results", "NPB_Birth_Weight_v4a.1.rdata"))
load(here::here("Results", "NPB_Birth_Weight_v4a.1.rdata"))
npb.sum <- summary(fit.npb)3.2.1 First, main effect regression coefficients with PIPs
rownames(npb.sum$main.effects) <- colnames(X.scaled[,-c(3)])
npb.sum$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## mean_pm -0.64125098 5.911603 -15.455836 10.490517 0.1816
## mean_o3 -126.48202072 96.518824 -285.016660 3.445415 0.8044
## pct_tree_cover -0.68083059 5.615548 -15.848685 10.739415 0.1900
## pct_impervious -2.83488760 8.796487 -29.792364 5.146130 0.2520
## mean_aadt_intensity -0.18793856 4.988127 -11.993448 10.921741 0.1692
## dist_m_tri -0.76891442 6.081892 -17.209786 10.305810 0.1928
## dist_m_npl 0.34958475 5.844586 -10.729199 14.822900 0.1804
## dist_m_waste_site 1.45511736 8.095672 -9.515091 26.912081 0.1968
## dist_m_major_emit -0.08282941 5.378265 -12.159189 12.434891 0.1872
## dist_m_cafo -4.47615039 22.150639 -62.347984 14.992358 0.2892
## dist_m_mine_well -2.67188258 9.303658 -32.030285 6.776363 0.2448
## cvd_rate_adj -2.62833089 8.514285 -29.765889 4.970325 0.2524
## res_rate_adj -3.01604247 9.570154 -32.440411 6.576391 0.2644
## violent_crime_rate -0.14945003 5.737088 -12.685065 11.958291 0.1824
## property_crime_rate -0.77234125 5.314391 -15.612152 8.053212 0.1860
## pct_less_hs -1.42774630 7.154552 -22.018857 8.044627 0.2156
## pct_unemp -23.79952093 28.421158 -87.511759 0.000000 0.6100
## pct_limited_eng -1.34682390 6.381113 -18.977246 7.841900 0.2012
## pct_hh_pov -1.24705339 7.810668 -22.139205 10.796265 0.2196
## pct_poc -1.54490752 8.140743 -22.840185 10.342720 0.23083.2.2 Next, posterior means and CIs for covariates
rownames(npb.sum$covariates)[2:nrow(npb.sum$covariates)] <- colnames(W.scaled2)
npb.sum$covariates## Posterior Mean SD 95% CI Lower 95% CI Upper
## <NA> 3142.948138 221.23796 2710.59014 3591.61617
## lat -8.852688 321.03802 -629.26824 598.31505
## lon 9.480748 153.06032 -279.27296 313.46058
## lat_lon_int 5.253298 387.46373 -747.98136 749.95032
## ed_no_hs 115.687118 76.71295 -32.87543 264.35342
## ed_hs 79.896671 69.27289 -57.10504 217.14594
## ed_aa 23.670895 60.11343 -94.17007 141.15205
## ed_4yr 67.124514 51.23803 -33.42328 169.58831
## low_bmi -72.184590 94.60050 -258.25729 119.68684
## ovwt_bmi 36.667903 41.33308 -41.92536 116.63096
## obese_bmi 112.604235 47.48015 18.38811 203.90394
## concep_spring -84.665927 101.94369 -239.82139 142.88394
## concep_summer -76.640630 131.37631 -336.69138 131.19268
## concep_fall -2.615382 89.46707 -183.37690 149.74649
## concep_2010 26.233351 217.00773 -417.31469 442.84115
## concep_2011 20.545505 215.93813 -408.59408 438.95755
## concep_2012 32.381563 216.32135 -402.50133 453.21728
## concep_2013 109.276001 217.54812 -315.18924 534.05497
## maternal_age 76.623361 22.76444 31.48236 121.65840
## any_smoker -140.725626 64.24669 -265.38100 -11.72093
## smokeSH -113.196362 44.47163 -200.08707 -26.22239
## mean_cpss 11.860854 20.41184 -26.66242 54.29258
## mean_epsd -51.380871 20.56738 -92.05272 -11.43408
## male 166.313157 34.15550 98.80753 230.260033.2.3 Interactions
Next, all of the interactions between exposures or between exposures and covariates
npb.sum$interactions## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] 0.017438215244 0.908986942 0.0000 0.0000 0.0012
## [2,] -0.001570933914 0.321889805 0.0000 0.0000 0.0012
## [3,] -0.005050155089 0.269284590 0.0000 0.0000 0.0008
## [4,] -0.000899881214 0.044994061 0.0000 0.0000 0.0004
## [5,] 0.001401134043 0.070056702 0.0000 0.0000 0.0004
## [6,] 0.006066131113 0.487992896 0.0000 0.0000 0.0020
## [7,] -0.002022843832 0.207040988 0.0000 0.0000 0.0008
## [8,] -0.003443891433 0.172194572 0.0000 0.0000 0.0004
## [9,] -0.012746513228 0.380095974 0.0000 0.0000 0.0016
## [10,] -0.012954477025 0.447726805 0.0000 0.0000 0.0012
## [11,] -0.007529079003 0.499802518 0.0000 0.0000 0.0020
## [12,] 0.004234366871 0.174822849 0.0000 0.0000 0.0008
## [13,] -0.000522542019 0.018663667 0.0000 0.0000 0.0008
## [14,] 0.002684209813 0.491394168 0.0000 0.0000 0.0016
## [15,] -0.002685413318 0.102346907 0.0000 0.0000 0.0008
## [16,] 0.003675129802 0.135131564 0.0000 0.0000 0.0008
## [17,] -0.021002092163 0.971540034 0.0000 0.0000 0.0012
## [18,] 0.010293649736 0.436031850 0.0000 0.0000 0.0008
## [19,] -0.003677054422 0.141189576 0.0000 0.0000 0.0008
## [20,] -0.013623634880 0.482453807 0.0000 0.0000 0.0020
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## [577,] -0.059857362648 2.821409134 0.0000 0.0000 0.0024
## [578,] -0.082423741515 2.711199122 0.0000 0.0000 0.0024
## [579,] -0.001539630212 0.135373632 0.0000 0.0000 0.0008
## [580,] -0.001881249357 0.102091001 0.0000 0.0000 0.0008
## [581,] -0.273424567937 4.702648379 0.0000 0.0000 0.0044
## [582,] -0.014882700089 1.074945145 0.0000 0.0000 0.0020
## [583,] -0.051432024167 1.498641348 0.0000 0.0000 0.0024
## [584,] -0.030154159928 1.313038874 0.0000 0.0000 0.0020
## [585,] -0.015113578472 0.927404907 0.0000 0.0000 0.0028
## [586,] 0.013488312390 0.529563578 0.0000 0.0000 0.0012
## [587,] -0.066288396181 1.942594865 0.0000 0.0000 0.0028
## [588,] 0.005366907139 0.509481097 0.0000 0.0000 0.0024
## [589,] -0.075516110774 3.081729763 0.0000 0.0000 0.0020
## [590,] -0.006622353921 0.305550680 0.0000 0.0000 0.0012
## [591,] 0.030377516261 1.381042758 0.0000 0.0000 0.0012
## [592,] -0.027925282276 1.703327605 0.0000 0.0000 0.0016
## [593,] -0.006673696594 0.796966429 0.0000 0.0000 0.0016
## [594,] -0.003944013945 0.404333389 0.0000 0.0000 0.0008
## [595,] 0.041033325033 1.410800229 0.0000 0.0000 0.0028
## [596,] -0.088249846552 2.585429286 0.0000 0.0000 0.0028
## [597,] 0.076040591351 2.087619634 0.0000 0.0000 0.0016
## [598,] -0.005347921639 0.299900920 0.0000 0.0000 0.0016
## [599,] -0.003443891433 0.172194572 0.0000 0.0000 0.0004
## [600,] -0.089966071692 2.943008324 0.0000 0.0000 0.0024
## [601,] -0.007537898449 0.509725000 0.0000 0.0000 0.0020
## [602,] 0.000355426098 0.102414359 0.0000 0.0000 0.0008
## [603,] 0.023383775505 0.768320558 0.0000 0.0000 0.0016
## [604,] -0.010267419005 0.582536774 0.0000 0.0000 0.0008
## [605,] 0.012836131413 0.476034309 0.0000 0.0000 0.0012
## [606,] -0.027646032585 0.885966621 0.0000 0.0000 0.0016
## [607,] -0.022748118392 1.029150878 0.0000 0.0000 0.0012
## [608,] -0.021068459704 1.133299454 0.0000 0.0000 0.0016
## [609,] -0.006110262875 0.191139753 0.0000 0.0000 0.0012
## [610,] -0.014722035733 1.005118281 0.0000 0.0000 0.0036
## [611,] 0.025729418296 0.814658457 0.0000 0.0000 0.0012
## [612,] 0.015125634248 0.955354419 0.0000 0.0000 0.0028
## [613,] -0.005630800949 0.380966473 0.0000 0.0000 0.0012
## [614,] 0.005567069839 0.813550005 0.0000 0.0000 0.0020
## [615,] -0.005487556507 0.200195669 0.0000 0.0000 0.0008
## [616,] -0.000506252733 0.025312637 0.0000 0.0000 0.0004
## [617,] -0.003764185227 0.371384972 0.0000 0.0000 0.0028
## [618,] 0.012134801995 0.606740100 0.0000 0.0000 0.0004
## [619,] -0.001384675744 0.178573365 0.0000 0.0000 0.0008
## [620,] 0.202873356065 4.580754569 0.0000 0.0000 0.0036
## [621,] -0.001983314158 0.099165708 0.0000 0.0000 0.0004
## [622,] 0.007013546677 0.255566204 0.0000 0.0000 0.0008
## [623,] -0.036270976639 1.822863150 0.0000 0.0000 0.0024
## [624,] 0.000848293967 0.183837266 0.0000 0.0000 0.0016
## [625,] -0.011977627499 0.425577713 0.0000 0.0000 0.0008
## [626,] -0.003217057662 0.332184789 0.0000 0.0000 0.0024
## [627,] 0.001749630365 0.087481518 0.0000 0.0000 0.0004
## [628,] -0.026009904267 0.796874583 0.0000 0.0000 0.0028
## [629,] -0.046105393163 1.461744462 0.0000 0.0000 0.0016
## [630,] -0.006275205220 0.604332575 0.0000 0.0000 0.0020
## [631,] -0.002603875800 0.302679952 0.0000 0.0000 0.0016
## [632,] 0.052034449028 2.375218521 0.0000 0.0000 0.0012
## [633,] -0.026511033843 1.144500222 0.0000 0.0000 0.0012
## [634,] -0.005099673018 0.254983651 0.0000 0.0000 0.0004
## [635,] -0.014182404061 0.886621189 0.0000 0.0000 0.0020
## [636,] 0.003110978758 0.155548938 0.0000 0.0000 0.0004
## [637,] -0.034119827898 1.089285569 0.0000 0.0000 0.0024
## [638,] -0.027586287285 1.709753842 0.0000 0.0000 0.0012
## [639,] 0.009966849736 0.410118400 0.0000 0.0000 0.0016
## [640,] -0.105488693433 2.663842527 0.0000 0.0000 0.0032
## [641,] -0.005135510457 0.354029314 0.0000 0.0000 0.0012
## [642,] -0.640510290189 8.719694453 0.0000 0.0000 0.0080
## [643,] 0.361484644902 6.896079382 0.0000 0.0000 0.0036
## [644,] -0.003489137480 0.447002294 0.0000 0.0000 0.0020
## [645,] -0.005109810825 0.255490541 0.0000 0.0000 0.0004
## [646,] -0.002286929002 0.709971694 0.0000 0.0000 0.0028
## [647,] -0.010898382309 0.385607247 0.0000 0.0000 0.0020
## [648,] -0.013898107209 0.674005366 0.0000 0.0000 0.0028
## [649,] -0.009880247074 0.342066072 0.0000 0.0000 0.0012
## [650,] 0.010660517262 0.459402439 0.0000 0.0000 0.00083.2.4 Predict fitted values for each individual
pred.npb <- predict(fit.npb)
fittedvals <- pred.npb$fitted.vals3.2.5 Plot predicted outcomes against “measured” outcomes
plot(fittedvals, Y)
abline(a = 0, b = 1, col = "red")
3.3 Run the NPB model with temperaure and ozone
Below I’ve used the set of priors labeled “24” and set scaleY = T
The priors are as follows: r priors.npb.24
Note that this version of the model does not include gest_age_w. It does include an indicator variable for season of conception (ref = winter) and the lon/lat as covariates and the percentage of the census tract population that is not NHW as an exposure.
priors.npb <- priors.npb.24
#' Exposures
colnames(X.scaled)## [1] "mean_pm" "mean_o3" "mean_temp"
## [4] "pct_tree_cover" "pct_impervious" "mean_aadt_intensity"
## [7] "dist_m_tri" "dist_m_npl" "dist_m_waste_site"
## [10] "dist_m_major_emit" "dist_m_cafo" "dist_m_mine_well"
## [13] "cvd_rate_adj" "res_rate_adj" "violent_crime_rate"
## [16] "property_crime_rate" "pct_less_hs" "pct_unemp"
## [19] "pct_limited_eng" "pct_hh_pov" "pct_poc"#' Covariates
colnames(W.scaled2)## [1] "lat" "lon" "lat_lon_int" "ed_no_hs"
## [5] "ed_hs" "ed_aa" "ed_4yr" "low_bmi"
## [9] "ovwt_bmi" "obese_bmi" "concep_spring" "concep_summer"
## [13] "concep_fall" "concep_2010" "concep_2011" "concep_2012"
## [17] "concep_2013" "maternal_age" "any_smoker" "smokeSH"
## [21] "mean_cpss" "mean_epsd" "male"# fit.npb2 <- npb(niter = 5000, nburn = 2500, X = X.scaled, Y = Y, W = W.scaled2,
# scaleY = TRUE,
# priors = priors.npb, interact = TRUE, XWinteract = TRUE)
# save(fit.npb2, file = here::here("Results", "NPB_Birth_Weight_v4a.2.rdata"))
load(here::here("Results", "NPB_Birth_Weight_v4a.2.rdata"))
npb.sum2 <- summary(fit.npb2)3.3.1 First, main effect regression coefficients with PIPs
rownames(npb.sum2$main.effects) <- colnames(X.scaled)
npb.sum2$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## mean_pm -6.4455763 14.489731 -51.36621 2.683216 0.3900
## mean_o3 -11.0042874 22.752166 -77.86027 2.341424 0.4668
## mean_temp -1.0527040 21.370684 -31.95659 15.886379 0.3216
## pct_tree_cover -2.0605910 6.449766 -19.12039 5.108510 0.2828
## pct_impervious -2.9374980 7.398262 -25.44654 1.796266 0.3024
## mean_aadt_intensity -0.8049048 5.433489 -14.31492 8.551697 0.2352
## dist_m_tri -2.1739110 6.890125 -21.93467 6.114000 0.2940
## dist_m_npl -0.9900659 5.268705 -14.29863 6.505562 0.2416
## dist_m_waste_site 0.4862897 7.223983 -11.84406 21.160154 0.2316
## dist_m_major_emit -0.8789868 5.184028 -14.26873 8.054941 0.2276
## dist_m_cafo -4.6180766 17.227018 -44.13164 9.197160 0.3720
## dist_m_mine_well -2.9322838 8.180628 -26.42892 5.800016 0.3208
## cvd_rate_adj -3.0336843 7.593749 -26.24958 4.104509 0.3336
## res_rate_adj -3.6478780 8.345746 -28.46638 2.910625 0.3524
## violent_crime_rate -1.0976867 5.955153 -15.26852 6.775785 0.2476
## property_crime_rate -2.1636489 6.153787 -19.26523 4.354570 0.2876
## pct_less_hs -3.1518381 8.226334 -26.93850 4.009727 0.3264
## pct_unemp -15.7384162 21.089822 -73.05732 0.000000 0.6156
## pct_limited_eng -2.5649220 7.175619 -23.53298 2.606821 0.2868
## pct_hh_pov -2.5735162 7.067605 -22.47381 2.354691 0.2944
## pct_poc -2.6849906 8.157365 -25.36287 4.181035 0.30363.3.2 Next, posterior means and CIs for covariates
rownames(npb.sum2$covariates)[2:nrow(npb.sum2$covariates)] <- colnames(W.scaled2)
npb.sum2$covariates## Posterior Mean SD 95% CI Lower 95% CI Upper
## <NA> 3158.7866392 218.49084 2738.15525 3591.270162
## lat -5.0778647 318.75678 -649.07654 598.794237
## lon -1.3163246 150.21131 -287.16996 301.070988
## lat_lon_int 0.9070337 383.25676 -771.57336 722.890601
## ed_no_hs 103.1285462 74.18587 -39.66910 245.517908
## ed_hs 76.2040362 66.87147 -55.56263 204.601927
## ed_aa 20.0923263 59.17875 -93.04662 135.665131
## ed_4yr 70.6485305 51.99147 -31.84932 170.862585
## low_bmi -70.4808587 92.21677 -253.62142 108.880019
## ovwt_bmi 43.3279289 39.76495 -36.11728 123.375098
## obese_bmi 119.2426138 44.62636 31.44680 205.620085
## concep_spring -82.6547585 55.25862 -186.16906 35.606865
## concep_summer -50.0030742 79.87508 -213.49674 91.265229
## concep_fall 70.9309202 66.48993 -56.25536 209.449908
## concep_2010 -1.2050533 217.99544 -433.49723 417.598929
## concep_2011 12.5723009 217.17112 -411.09172 433.388265
## concep_2012 70.6052139 217.48723 -351.09090 492.224084
## concep_2013 129.9476757 214.70349 -287.84362 529.665067
## maternal_age 69.4292496 21.80828 25.79014 110.086956
## any_smoker -162.9538912 62.46679 -289.55835 -42.591510
## smokeSH -82.2831407 43.82815 -171.61774 1.782190
## mean_cpss 3.1369961 19.19174 -33.38475 41.404436
## mean_epsd -43.9248511 19.84420 -81.46977 -4.993641
## male 171.9552244 31.88727 106.91092 234.4151503.3.3 Interactions
Next, all of the interactions between exposures or between exposures and covariates
npb.sum2$interactions## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] 1.194658926659 8.57711879 0.00000 0.0000 0.0216
## [2,] 1.052533086230 8.03807503 0.00000 0.0000 0.0200
## [3,] -0.003185446482 0.92512170 0.00000 0.0000 0.0024
## [4,] -0.018234201891 0.52129268 0.00000 0.0000 0.0016
## [5,] 0.014956771419 0.49698695 0.00000 0.0000 0.0012
## [6,] -0.004561501319 0.36148257 0.00000 0.0000 0.0028
## [7,] -0.018155212716 0.59266879 0.00000 0.0000 0.0020
## [8,] -0.012546584738 0.44681547 0.00000 0.0000 0.0016
## [9,] -0.016837852880 0.45595145 0.00000 0.0000 0.0036
## [10,] -0.042703830606 0.82466283 0.00000 0.0000 0.0036
## [11,] 0.001608820602 0.34180533 0.00000 0.0000 0.0028
## [12,] -0.021844129742 0.56526999 0.00000 0.0000 0.0028
## [13,] -0.009765518433 0.39451776 0.00000 0.0000 0.0032
## [14,] -0.035696541157 0.77000573 0.00000 0.0000 0.0032
## [15,] -0.002621529365 0.27549081 0.00000 0.0000 0.0008
## [16,] -0.033604211639 0.78382068 0.00000 0.0000 0.0040
## [17,] -0.013301097351 0.42436228 0.00000 0.0000 0.0016
## [18,] -0.090105690587 1.69999876 0.00000 0.0000 0.0056
## [19,] -0.005049895956 0.19066975 0.00000 0.0000 0.0008
## [20,] -0.014803432043 0.67378729 0.00000 0.0000 0.0032
## [21,] -171.586953546664 32.64089047 -241.01292 -120.2583 1.0000
## [22,] -0.013635922495 0.35496660 0.00000 0.0000 0.0020
## [23,] -0.012682016081 0.39454924 0.00000 0.0000 0.0016
## [24,] -0.003734548575 0.42229682 0.00000 0.0000 0.0012
## [25,] -0.029055286362 0.67199799 0.00000 0.0000 0.0028
## [26,] -0.018132591417 0.52436740 0.00000 0.0000 0.0016
## [27,] -0.113254844358 1.90957615 0.00000 0.0000 0.0052
## [28,] -0.006644755107 0.46889824 0.00000 0.0000 0.0016
## [29,] -0.009598516058 0.34205166 0.00000 0.0000 0.0008
## [30,] -0.034347717584 0.85181540 0.00000 0.0000 0.0028
## [31,] 0.011819037075 0.56315276 0.00000 0.0000 0.0020
## [32,] -0.003461516042 0.20446331 0.00000 0.0000 0.0008
## [33,] -0.005769212102 0.18179199 0.00000 0.0000 0.0012
## [34,] 0.000000000000 0.00000000 0.00000 0.0000 0.0000
## [35,] 0.034329455299 1.02874325 0.00000 0.0000 0.0032
## [36,] 0.032492362349 1.03409558 0.00000 0.0000 0.0016
## [37,] 0.000891031862 0.08448097 0.00000 0.0000 0.0012
## [38,] 0.090980960008 2.21371528 0.00000 0.0000 0.0028
## [39,] -0.010382011432 0.36864675 0.00000 0.0000 0.0020
## [40,] -0.016138476375 0.41620817 0.00000 0.0000 0.0024
## [41,] -0.009839010850 0.48059257 0.00000 0.0000 0.0012
## [42,] 0.008104598286 0.22550419 0.00000 0.0000 0.0016
## [43,] -0.013429211899 0.57948800 0.00000 0.0000 0.0048
## [44,] -0.003394295259 0.28235672 0.00000 0.0000 0.0012
## [45,] -0.042573667130 0.95713794 0.00000 0.0000 0.0044
## [46,] -0.000826406587 0.40118896 0.00000 0.0000 0.0020
## [47,] -0.026966543148 0.75806092 0.00000 0.0000 0.0032
## [48,] -0.007680688178 0.21704419 0.00000 0.0000 0.0016
## [49,] 0.008117026562 0.87097121 0.00000 0.0000 0.0020
## [50,] 0.006346531419 0.38928508 0.00000 0.0000 0.0016
## [51,] -0.021299448942 0.55958888 0.00000 0.0000 0.0024
## [52,] 0.013693274673 1.02422534 0.00000 0.0000 0.0016
## [53,] 0.024996903348 1.08308278 0.00000 0.0000 0.0024
## [54,] 0.018574679160 0.94261883 0.00000 0.0000 0.0016
## [55,] -0.024362560567 0.57485796 0.00000 0.0000 0.0028
## [56,] 0.001678042324 0.37343646 0.00000 0.0000 0.0016
## [57,] -0.003953868511 0.16685696 0.00000 0.0000 0.0012
## [58,] -0.004799610070 0.25122579 0.00000 0.0000 0.0008
## [59,] -0.013293622476 0.55843588 0.00000 0.0000 0.0020
## [60,] -0.008947024374 0.54136289 0.00000 0.0000 0.0024
## [61,] -0.031357955854 1.06565322 0.00000 0.0000 0.0028
## [62,] 0.015880659888 0.66992662 0.00000 0.0000 0.0024
## [63,] 0.040153744116 1.67909645 0.00000 0.0000 0.0028
## [64,] -0.020421245428 0.54028258 0.00000 0.0000 0.0028
## [65,] -0.016600414772 0.40215708 0.00000 0.0000 0.0028
## [66,] 0.000832641679 0.03198112 0.00000 0.0000 0.0012
## [67,] 0.000313880310 0.13587445 0.00000 0.0000 0.0016
## [68,] -0.012904860091 0.33997237 0.00000 0.0000 0.0016
## [69,] -0.012906985427 0.37150742 0.00000 0.0000 0.0024
## [70,] -0.014995334410 0.45596885 0.00000 0.0000 0.0020
## [71,] -0.008608882464 0.46065656 0.00000 0.0000 0.0008
## [72,] 0.003825531837 0.41208515 0.00000 0.0000 0.0008
## [73,] 0.025834609207 0.76024914 0.00000 0.0000 0.0016
## [74,] -0.004848640804 0.19505860 0.00000 0.0000 0.0008
## [75,] -0.000423103699 0.66000525 0.00000 0.0000 0.0016
## [76,] 0.007639130633 0.41240669 0.00000 0.0000 0.0028
## [77,] 0.003876165318 0.59269436 0.00000 0.0000 0.0012
## [78,] -0.001811329169 0.31879677 0.00000 0.0000 0.0020
## [79,] -0.003734793780 0.18673969 0.00000 0.0000 0.0004
## [80,] -0.027933645383 0.68769370 0.00000 0.0000 0.0024
## [81,] 0.002650860284 0.57650950 0.00000 0.0000 0.0024
## [82,] -0.016887597673 0.43320387 0.00000 0.0000 0.0016
## [83,] -0.019308661504 0.95671561 0.00000 0.0000 0.0020
## [84,] 0.000330648547 0.14159500 0.00000 0.0000 0.0008
## [85,] -0.013388069237 0.51592470 0.00000 0.0000 0.0028
## [86,] -0.014441395277 0.51131969 0.00000 0.0000 0.0024
## [87,] -0.008416476950 0.26162437 0.00000 0.0000 0.0016
## [88,] -0.005732547922 0.20673934 0.00000 0.0000 0.0012
## [89,] -0.000857799082 0.05895210 0.00000 0.0000 0.0008
## [90,] 0.000683600453 0.03418002 0.00000 0.0000 0.0004
## [91,] 0.003851299075 0.38392497 0.00000 0.0000 0.0016
## [92,] -0.007454980732 0.41341438 0.00000 0.0000 0.0016
## [93,] 0.015001946600 0.43997718 0.00000 0.0000 0.0016
## [94,] 0.017991156456 0.70262373 0.00000 0.0000 0.0024
## [95,] -0.015076054331 0.73672139 0.00000 0.0000 0.0020
## [96,] -0.002107585358 0.14812449 0.00000 0.0000 0.0012
## [97,] -0.009268562489 0.38915641 0.00000 0.0000 0.0028
## [98,] -0.018475394186 0.49671920 0.00000 0.0000 0.0016
## [99,] -0.010059720923 0.41898146 0.00000 0.0000 0.0032
## [100,] -0.022049857681 0.66317079 0.00000 0.0000 0.0024
## [101,] -0.000393655823 0.34043129 0.00000 0.0000 0.0016
## [102,] -0.015397807544 0.47746187 0.00000 0.0000 0.0020
## [103,] 0.001272539714 0.23593355 0.00000 0.0000 0.0016
## [104,] -0.009892363892 0.59665144 0.00000 0.0000 0.0020
## [105,] 0.007747953187 0.33554846 0.00000 0.0000 0.0008
## [106,] -0.004709086305 0.17474516 0.00000 0.0000 0.0008
## [107,] -0.000460775722 0.44833311 0.00000 0.0000 0.0024
## [108,] -0.004805551141 0.56405991 0.00000 0.0000 0.0020
## [109,] 0.001923025411 0.28114255 0.00000 0.0000 0.0024
## [110,] -0.006284330981 0.35295907 0.00000 0.0000 0.0016
## [111,] 0.015440379558 1.07384143 0.00000 0.0000 0.0032
## [112,] 0.004602746801 0.56758717 0.00000 0.0000 0.0028
## [113,] -0.017735981111 0.54082001 0.00000 0.0000 0.0012
## [114,] -0.010477644173 0.35254096 0.00000 0.0000 0.0016
## [115,] -0.004642558155 0.13795289 0.00000 0.0000 0.0020
## [116,] 0.033984364493 1.00079740 0.00000 0.0000 0.0016
## [117,] 0.005451446967 0.58457171 0.00000 0.0000 0.0020
## [118,] 0.035349518956 1.06691479 0.00000 0.0000 0.0020
## [119,] -0.003648434595 0.50870251 0.00000 0.0000 0.0020
## [120,] -0.000406517433 0.55694524 0.00000 0.0000 0.0036
## [121,] -0.000963162730 0.04815814 0.00000 0.0000 0.0004
## [122,] -0.010886914652 0.29603307 0.00000 0.0000 0.0020
## [123,] -0.004181084324 0.20905422 0.00000 0.0000 0.0004
## [124,] -0.002813651968 0.15860679 0.00000 0.0000 0.0016
## [125,] 0.002412117795 0.07549225 0.00000 0.0000 0.0012
## [126,] 0.001875640973 0.22705145 0.00000 0.0000 0.0008
## [127,] 0.008956258568 0.42606253 0.00000 0.0000 0.0016
## [128,] -0.005605121654 0.31091848 0.00000 0.0000 0.0008
## [129,] -0.021503640232 0.60632185 0.00000 0.0000 0.0020
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## [684,] 0.004567504779 0.67764079 0.00000 0.0000 0.0020
## [685,] -1.754547128681 15.22012268 0.00000 0.0000 0.0156
## [686,] 1.653403614093 13.90185621 0.00000 0.0000 0.0188
## [687,] -0.068474491864 2.52800112 0.00000 0.0000 0.0028
## [688,] 0.001661340212 0.36765531 0.00000 0.0000 0.0024
## [689,] -0.182967651174 5.65166770 0.00000 0.0000 0.0036
## [690,] -0.008267804300 0.59744544 0.00000 0.0000 0.0032
## [691,] -0.015746654977 0.50950701 0.00000 0.0000 0.0020
## [692,] -0.008984176592 0.28700121 0.00000 0.0000 0.0012
## [693,] -0.012934723969 0.40373791 0.00000 0.0000 0.00163.3.4 Predict fitted values for each individual
pred.npb2 <- predict(fit.npb2)
fittedvals2 <- pred.npb2$fitted.vals3.3.5 Plot predicted outcomes against “measured” outcomes
plot(fittedvals2, Y)
abline(a = 0, b = 1, col = "red")
3.4 Fit the NPB model without ozone and with temperature
Only ozone shows up in the NPB model. However, there is some speculation that ozone is just a proxy for some of the other variables. Here I am running the NPB model without ozone but with temperature just to see if something else pops up instead.
priors.npb <- priors.npb.24
#' Exposures
colnames(X.scaled)## [1] "mean_pm" "mean_o3" "mean_temp"
## [4] "pct_tree_cover" "pct_impervious" "mean_aadt_intensity"
## [7] "dist_m_tri" "dist_m_npl" "dist_m_waste_site"
## [10] "dist_m_major_emit" "dist_m_cafo" "dist_m_mine_well"
## [13] "cvd_rate_adj" "res_rate_adj" "violent_crime_rate"
## [16] "property_crime_rate" "pct_less_hs" "pct_unemp"
## [19] "pct_limited_eng" "pct_hh_pov" "pct_poc"#' Covariates
colnames(W.scaled2)## [1] "lat" "lon" "lat_lon_int" "ed_no_hs"
## [5] "ed_hs" "ed_aa" "ed_4yr" "low_bmi"
## [9] "ovwt_bmi" "obese_bmi" "concep_spring" "concep_summer"
## [13] "concep_fall" "concep_2010" "concep_2011" "concep_2012"
## [17] "concep_2013" "maternal_age" "any_smoker" "smokeSH"
## [21] "mean_cpss" "mean_epsd" "male"# fit.npb3 <- npb(niter = 5000, nburn = 2500, X = X.scaled[,-c(2)], Y = Y, W = W.scaled2,
# scaleY = TRUE,
# priors = priors.npb, interact = TRUE, XWinteract = TRUE)
# save(fit.npb3, file = here::here("Results", "NPB_Birth_Weight_v4a.3.rdata"))
load(here::here("Results", "NPB_Birth_Weight_v4a.3.rdata"))
npb.sum3 <- summary(fit.npb3)3.4.1 First, main effect regression coefficients with PIPs
rownames(npb.sum3$main.effects) <- colnames(X.scaled[,-c(2)])
npb.sum3$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## mean_pm -6.2270028 11.829903 -40.83325 1.3329720 0.4216
## mean_temp -5.9078416 14.521641 -48.41181 3.9188396 0.3936
## pct_tree_cover -1.9400109 6.176479 -18.85633 5.1386887 0.2768
## pct_impervious -3.8993339 8.193060 -28.11322 0.6778887 0.3512
## mean_aadt_intensity -1.2645979 5.587482 -15.30176 6.5179151 0.2332
## dist_m_tri -1.8403906 7.008697 -21.51611 9.4004148 0.2732
## dist_m_npl -0.6330595 6.362851 -15.29715 12.8578425 0.2448
## dist_m_waste_site -0.4297864 6.516643 -14.28281 13.9915356 0.2332
## dist_m_major_emit -0.5368893 6.054691 -13.79800 11.8574575 0.2272
## dist_m_cafo -3.3788146 13.135915 -32.52030 8.8764179 0.3396
## dist_m_mine_well -4.9812807 10.496138 -35.19974 2.8591574 0.3868
## cvd_rate_adj -4.0803243 9.027007 -29.75359 2.0091130 0.3660
## res_rate_adj -4.6358931 9.454517 -31.85015 1.8292630 0.3928
## violent_crime_rate -1.1196381 6.014000 -16.29494 7.4135878 0.2476
## property_crime_rate -2.1919509 6.251015 -18.80068 2.8857337 0.2760
## pct_less_hs -2.9564607 7.425378 -24.09712 4.3310094 0.3324
## pct_unemp -12.3136410 17.898237 -62.01418 0.0000000 0.5756
## pct_limited_eng -2.4849233 7.052612 -21.98537 3.2781220 0.2932
## pct_hh_pov -2.2683344 6.679594 -19.73307 4.6395661 0.2964
## pct_poc -3.0137492 7.665084 -25.22988 3.7484350 0.31803.4.2 Next, posterior means and CIs for covariates
rownames(npb.sum3$covariates)[2:nrow(npb.sum3$covariates)] <- colnames(W.scaled2)
npb.sum3$covariates## Posterior Mean SD 95% CI Lower 95% CI Upper
## <NA> 3058.442273 219.05707 2620.58039 3498.442014
## lat -5.999754 318.89735 -608.36191 623.377269
## lon 10.546695 152.15860 -288.06563 299.195424
## lat_lon_int 7.195182 385.14524 -728.60902 776.523923
## ed_no_hs 128.616117 74.63545 -18.48899 272.062718
## ed_hs 95.741646 66.78362 -34.93224 225.182912
## ed_aa 39.261940 59.36616 -77.55912 152.325102
## ed_4yr 72.228575 50.91669 -26.20372 174.118664
## low_bmi -65.473942 92.40772 -247.48219 119.485254
## ovwt_bmi 37.317858 39.20717 -39.40143 112.156034
## obese_bmi 100.422704 45.68430 8.69515 187.501340
## concep_spring 341.338572 78.56078 188.12131 496.239239
## concep_summer 59.381409 50.90035 -41.29376 154.152368
## concep_fall 357.791243 78.83716 204.71163 502.817734
## concep_2010 -4.131619 216.93677 -447.85147 415.492330
## concep_2011 -63.978522 216.63831 -492.09241 367.394511
## concep_2012 3.946398 216.53151 -434.74359 427.725231
## concep_2013 55.121301 215.79316 -376.40130 483.566588
## maternal_age 81.511954 21.99303 39.50672 125.837419
## any_smoker -137.171944 60.97173 -255.55101 -15.501723
## smokeSH -111.126885 42.72822 -194.76406 -27.370965
## mean_cpss 11.338319 19.24256 -25.76778 49.134449
## mean_epsd -45.061018 20.08659 -83.95663 -4.903774
## male 167.351395 33.20811 103.51980 230.9233443.4.3 Interactions
Next, all of the interactions between exposures or between exposures and covariates
npb.sum3$interactions## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] -0.000376303369 0.25387243 0.0000 0.0000 0.0024
## [2,] -0.006764598353 0.33397270 0.0000 0.0000 0.0024
## [3,] -0.006935068553 0.22970068 0.0000 0.0000 0.0020
## [4,] 0.015805756547 0.60557707 0.0000 0.0000 0.0012
## [5,] -0.006043426468 0.17538887 0.0000 0.0000 0.0012
## [6,] 0.001295340895 0.45616661 0.0000 0.0000 0.0028
## [7,] -0.017682733203 0.43962863 0.0000 0.0000 0.0024
## [8,] -0.007409563610 0.57893001 0.0000 0.0000 0.0060
## [9,] -0.019516770679 0.47299718 0.0000 0.0000 0.0028
## [10,] -0.013874626769 0.33988058 0.0000 0.0000 0.0032
## [11,] -0.011215927711 0.30262510 0.0000 0.0000 0.0028
## [12,] -0.017190382562 0.63066133 0.0000 0.0000 0.0032
## [13,] -0.014081172487 0.39448411 0.0000 0.0000 0.0032
## [14,] -0.004728048444 0.43587946 0.0000 0.0000 0.0012
## [15,] -0.058079904175 1.37959511 0.0000 0.0000 0.0044
## [16,] 0.001544616464 0.42371313 0.0000 0.0000 0.0020
## [17,] -0.040732695240 0.86986619 0.0000 0.0000 0.0044
## [18,] -0.006865557049 0.21533116 0.0000 0.0000 0.0024
## [19,] -0.011998894558 0.43182955 0.0000 0.0000 0.0032
## [20,] -0.008361691197 0.30970124 0.0000 0.0000 0.0028
## [21,] -0.006970104828 0.26660794 0.0000 0.0000 0.0028
## [22,] -0.007007965690 0.23325519 0.0000 0.0000 0.0016
## [23,] -0.040396262965 0.63565151 0.0000 0.0000 0.0060
## [24,] -0.020959624209 0.54080109 0.0000 0.0000 0.0024
## [25,] -0.021724730863 0.51478822 0.0000 0.0000 0.0032
## [26,] -0.005413860447 0.18892482 0.0000 0.0000 0.0016
## [27,] -0.029738397069 0.55751700 0.0000 0.0000 0.0044
## [28,] -0.023196115574 0.79488927 0.0000 0.0000 0.0028
## [29,] 0.008410026464 0.31443422 0.0000 0.0000 0.0028
## [30,] 0.005992522844 0.52089383 0.0000 0.0000 0.0036
## [31,] -0.010836618074 0.46832319 0.0000 0.0000 0.0020
## [32,] -0.019366941514 0.41092647 0.0000 0.0000 0.0040
## [33,] -0.007073964709 0.35369824 0.0000 0.0000 0.0004
## [34,] -0.009533040841 0.20545456 0.0000 0.0000 0.0024
## [35,] -0.002044884670 0.11064865 0.0000 0.0000 0.0016
## [36,] 0.017846464403 0.49706980 0.0000 0.0000 0.0032
## [37,] -0.001511884657 0.25735825 0.0000 0.0000 0.0016
## [38,] -0.000547793286 0.48696232 0.0000 0.0000 0.0032
## [39,] -0.003269810596 0.26115267 0.0000 0.0000 0.0020
## [40,] -0.004214310639 0.19912010 0.0000 0.0000 0.0024
## [41,] -0.028704990271 0.74822170 0.0000 0.0000 0.0040
## [42,] -0.015029729977 0.37392663 0.0000 0.0000 0.0032
## [43,] 0.029835510680 0.91802632 0.0000 0.0000 0.0024
## [44,] -0.017132728645 0.37365305 0.0000 0.0000 0.0032
## [45,] -0.026701494317 0.82838209 0.0000 0.0000 0.0040
## [46,] -0.020654201914 0.79934797 0.0000 0.0000 0.0032
## [47,] -0.004008427956 0.59029421 0.0000 0.0000 0.0028
## [48,] -0.029563544537 0.69968752 0.0000 0.0000 0.0032
## [49,] -0.009712658446 0.71668238 0.0000 0.0000 0.0032
## [50,] 0.005051140838 0.51037439 0.0000 0.0000 0.0028
## [51,] -0.011254438821 0.29627706 0.0000 0.0000 0.0032
## [52,] 0.003964949062 0.35243090 0.0000 0.0000 0.0020
## [53,] 0.046573381788 1.74459203 0.0000 0.0000 0.0040
## [54,] -0.007312324753 0.21243923 0.0000 0.0000 0.0024
## [55,] -0.011627855194 0.66265755 0.0000 0.0000 0.0028
## [56,] 0.010200989337 0.47201164 0.0000 0.0000 0.0024
## [57,] -0.009058233473 0.28611041 0.0000 0.0000 0.0024
## [58,] 0.012503107309 0.64921487 0.0000 0.0000 0.0028
## [59,] 0.008498426314 0.55861658 0.0000 0.0000 0.0028
## [60,] -0.013857988794 0.34216890 0.0000 0.0000 0.0032
## [61,] -0.002599128811 0.14283681 0.0000 0.0000 0.0020
## [62,] -0.033409361123 0.85233212 0.0000 0.0000 0.0036
## [63,] -0.027676783795 0.92896280 0.0000 0.0000 0.0032
## [64,] -0.000659140940 0.25364346 0.0000 0.0000 0.0020
## [65,] 0.001733394974 0.22635175 0.0000 0.0000 0.0016
## [66,] -0.007860807829 0.23076469 0.0000 0.0000 0.0016
## [67,] -0.011956818583 0.37250283 0.0000 0.0000 0.0032
## [68,] 0.000937261816 0.14082938 0.0000 0.0000 0.0020
## [69,] -0.006423707867 0.30986026 0.0000 0.0000 0.0024
## [70,] -0.017475748447 0.42127434 0.0000 0.0000 0.0024
## [71,] 0.012804709078 0.45629833 0.0000 0.0000 0.0032
## [72,] -0.001671314769 0.17985171 0.0000 0.0000 0.0016
## [73,] 0.000658612632 0.43937082 0.0000 0.0000 0.0020
## [74,] 0.017420848461 0.60014008 0.0000 0.0000 0.0016
## [75,] -0.020080414204 0.45119462 0.0000 0.0000 0.0028
## [76,] -0.008851317288 0.40565163 0.0000 0.0000 0.0032
## [77,] -0.011723376751 0.38630949 0.0000 0.0000 0.0020
## [78,] -0.041340352835 0.92628545 0.0000 0.0000 0.0060
## [79,] -0.032336387805 0.64657739 0.0000 0.0000 0.0044
## [80,] -0.025940433076 0.53424941 0.0000 0.0000 0.0044
## [81,] -0.006915207656 0.26363331 0.0000 0.0000 0.0024
## [82,] -0.016584083503 0.88943253 0.0000 0.0000 0.0020
## [83,] -0.004386522652 0.34890949 0.0000 0.0000 0.0016
## [84,] -0.005602540932 0.30335672 0.0000 0.0000 0.0020
## [85,] 0.028464118672 0.69765595 0.0000 0.0000 0.0036
## [86,] 0.002222104801 0.37119891 0.0000 0.0000 0.0056
## [87,] -0.007093243740 0.20921444 0.0000 0.0000 0.0012
## [88,] -0.004806214644 0.20942333 0.0000 0.0000 0.0024
## [89,] -0.008151481768 0.21045392 0.0000 0.0000 0.0024
## [90,] 0.001062292648 0.22314458 0.0000 0.0000 0.0016
## [91,] 0.006050744360 0.49987919 0.0000 0.0000 0.0032
## [92,] -0.009631324061 0.54801399 0.0000 0.0000 0.0012
## [93,] -0.005515533266 0.17387850 0.0000 0.0000 0.0012
## [94,] -0.002598558231 0.18080552 0.0000 0.0000 0.0020
## [95,] 0.002378794456 0.11893972 0.0000 0.0000 0.0004
## [96,] 0.013454093375 0.42284519 0.0000 0.0000 0.0028
## [97,] -0.006020974326 0.26723311 0.0000 0.0000 0.0008
## [98,] -0.007388329221 0.29598010 0.0000 0.0000 0.0016
## [99,] -0.005488423861 0.37897275 0.0000 0.0000 0.0020
## [100,] 0.000347217318 0.42933808 0.0000 0.0000 0.0016
## [101,] -0.002676813019 0.15342417 0.0000 0.0000 0.0012
## [102,] -0.005627925173 0.25175851 0.0000 0.0000 0.0024
## [103,] -0.011844692290 0.48027738 0.0000 0.0000 0.0032
## [104,] -0.001268329736 0.14999299 0.0000 0.0000 0.0016
## [105,] -0.001045182003 0.29266520 0.0000 0.0000 0.0024
## [106,] -0.008521510789 0.25306641 0.0000 0.0000 0.0036
## [107,] -0.001607109386 0.46397777 0.0000 0.0000 0.0020
## [108,] -0.002991057059 0.32306413 0.0000 0.0000 0.0012
## [109,] -0.013203907129 0.26653563 0.0000 0.0000 0.0028
## [110,] -0.006752793322 0.24854685 0.0000 0.0000 0.0020
## [111,] -0.002074205569 0.18650003 0.0000 0.0000 0.0016
## [112,] -0.008867585724 0.42849060 0.0000 0.0000 0.0032
## [113,] 0.022057077844 0.71094971 0.0000 0.0000 0.0016
## [114,] 0.009018884773 0.47724739 0.0000 0.0000 0.0020
## [115,] -0.008619826009 0.22575406 0.0000 0.0000 0.0016
## [116,] -0.017847765307 0.50532511 0.0000 0.0000 0.0060
## [117,] -0.015248694595 0.33725528 0.0000 0.0000 0.0048
## [118,] -0.000074774992 0.12451043 0.0000 0.0000 0.0012
## [119,] -0.003282572593 0.18213451 0.0000 0.0000 0.0008
## [120,] -0.003751740166 0.14635147 0.0000 0.0000 0.0012
## [121,] -0.007847722896 0.26958008 0.0000 0.0000 0.0028
## [122,] 0.006653098385 0.22623174 0.0000 0.0000 0.0016
## [123,] 0.012660124049 0.45883245 0.0000 0.0000 0.0032
## [124,] -0.019623772516 0.54933169 0.0000 0.0000 0.0032
## [125,] 0.009684540682 0.42251469 0.0000 0.0000 0.0020
## [126,] 0.008427422254 0.24225644 0.0000 0.0000 0.0036
## [127,] 0.009363123779 0.35982593 0.0000 0.0000 0.0040
## [128,] -0.005542629144 0.14901338 0.0000 0.0000 0.0020
## [129,] -0.016123626620 0.38449148 0.0000 0.0000 0.0032
## [130,] -0.001244918327 0.34023677 0.0000 0.0000 0.0016
## [131,] -0.029894041262 1.06363563 0.0000 0.0000 0.0024
## [132,] -0.004302471753 0.25635804 0.0000 0.0000 0.0020
## [133,] -0.019760522392 0.64591174 0.0000 0.0000 0.0028
## [134,] -0.000079460152 0.35183797 0.0000 0.0000 0.0020
## [135,] -0.021561690494 0.52154819 0.0000 0.0000 0.0040
## [136,] -0.010555391033 0.45399201 0.0000 0.0000 0.0032
## [137,] -0.010336818633 0.34601287 0.0000 0.0000 0.0032
## [138,] -0.012928137021 0.46364328 0.0000 0.0000 0.0032
## [139,] -0.006323032973 0.20545899 0.0000 0.0000 0.0032
## [140,] -0.018984635457 0.40891705 0.0000 0.0000 0.0040
## [141,] 0.008257402372 0.28602969 0.0000 0.0000 0.0028
## [142,] -0.017586561025 0.79359099 0.0000 0.0000 0.0020
## [143,] 0.015017855215 0.91237201 0.0000 0.0000 0.0012
## [144,] -0.013311670511 0.43429038 0.0000 0.0000 0.0028
## [145,] -0.006586659401 0.53689941 0.0000 0.0000 0.0028
## [146,] 0.003999576191 0.24275307 0.0000 0.0000 0.0016
## [147,] -0.000294332761 0.44241578 0.0000 0.0000 0.0032
## [148,] 0.005244980228 0.57523955 0.0000 0.0000 0.0032
## [149,] -0.013032968794 0.36970504 0.0000 0.0000 0.0016
## [150,] -0.003917044902 0.12556602 0.0000 0.0000 0.0020
## [151,] 0.005781301796 0.24331267 0.0000 0.0000 0.0012
## [152,] 0.284933306458 4.49136701 0.0000 0.0000 0.0076
## [153,] 0.014326929783 0.54250773 0.0000 0.0000 0.0020
## [154,] 0.047834466525 1.16532937 0.0000 0.0000 0.0044
## [155,] -0.002551890086 0.09171732 0.0000 0.0000 0.0008
## [156,] -0.021328488629 0.42952927 0.0000 0.0000 0.0032
## [157,] -0.017699617516 0.53203310 0.0000 0.0000 0.0036
## [158,] -0.012172056095 0.39001156 0.0000 0.0000 0.0016
## [159,] -0.072518520013 1.12115609 0.0000 0.0000 0.0052
## [160,] -0.049943378059 1.01841364 0.0000 0.0000 0.0044
## [161,] -0.016273023996 0.41280465 0.0000 0.0000 0.0036
## [162,] 0.001403457231 0.33030159 0.0000 0.0000 0.0020
## [163,] 0.001034070682 0.09571430 0.0000 0.0000 0.0008
## [164,] -0.002312992549 0.08391387 0.0000 0.0000 0.0012
## [165,] -0.014058402906 0.33647727 0.0000 0.0000 0.0032
## [166,] -0.024069094626 0.64577300 0.0000 0.0000 0.0036
## [167,] -0.012639900567 0.68511098 0.0000 0.0000 0.0016
## [168,] -0.057545954671 1.33160866 0.0000 0.0000 0.0048
## [169,] -0.004369740508 0.27642141 0.0000 0.0000 0.0020
## [170,] 0.000249790060 0.01033581 0.0000 0.0000 0.0008
## [171,] -0.004814476616 0.27785058 0.0000 0.0000 0.0020
## [172,] 0.003322371715 0.28304937 0.0000 0.0000 0.0024
## [173,] 0.000262044135 0.34686150 0.0000 0.0000 0.0036
## [174,] 0.000871106246 0.17484055 0.0000 0.0000 0.0016
## [175,] -0.011997385424 0.52003894 0.0000 0.0000 0.0024
## [176,] 0.000257900068 0.23451631 0.0000 0.0000 0.0016
## [177,] -0.005419969107 0.19064744 0.0000 0.0000 0.0016
## [178,] -0.005491961553 0.14912357 0.0000 0.0000 0.0016
## [179,] -0.006607039834 0.24645460 0.0000 0.0000 0.0028
## [180,] -0.029074198672 0.95631617 0.0000 0.0000 0.0052
## [181,] -0.005154792508 0.28380396 0.0000 0.0000 0.0020
## [182,] -0.005153860213 0.24098062 0.0000 0.0000 0.0020
## [183,] 0.013663074266 0.64420976 0.0000 0.0000 0.0040
## [184,] -0.011605194220 0.37096131 0.0000 0.0000 0.0052
## [185,] -0.013849934083 0.36826136 0.0000 0.0000 0.0024
## [186,] -0.006033723166 0.25128820 0.0000 0.0000 0.0028
## [187,] -0.017259157601 0.37064532 0.0000 0.0000 0.0044
## [188,] -0.003139894166 0.28067924 0.0000 0.0000 0.0040
## [189,] -0.002519755325 0.81605617 0.0000 0.0000 0.0032
## [190,] 0.008864952351 0.56598057 0.0000 0.0000 0.0040
## [191,] 0.005384770334 0.25875965 0.0000 0.0000 0.0012
## [192,] 0.007138326893 0.55395280 0.0000 0.0000 0.0020
## [193,] -0.017840666323 0.50828940 0.0000 0.0000 0.0028
## [194,] 0.001591985921 0.44204808 0.0000 0.0000 0.0028
## [195,] -0.035300528439 0.82261060 0.0000 0.0000 0.0044
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## [471,] -0.031141800176 0.80489472 0.0000 0.0000 0.0028
## [472,] -0.005892461845 0.33006215 0.0000 0.0000 0.0048
## [473,] -0.083986658901 2.63104402 0.0000 0.0000 0.0036
## [474,] -0.008533810773 0.23221115 0.0000 0.0000 0.0024
## [475,] 0.003686971151 0.78069158 0.0000 0.0000 0.0048
## [476,] -0.003163797113 0.62938739 0.0000 0.0000 0.0040
## [477,] -0.006147636056 0.27839611 0.0000 0.0000 0.0040
## [478,] -0.007780992008 0.39661424 0.0000 0.0000 0.0036
## [479,] -0.093984490440 2.33804116 0.0000 0.0000 0.0036
## [480,] -0.142000201014 3.19632623 0.0000 0.0000 0.0052
## [481,] -0.060769728387 1.80837064 0.0000 0.0000 0.0024
## [482,] 0.249961276510 5.58804373 0.0000 0.0000 0.0044
## [483,] -0.014810988996 0.56133080 0.0000 0.0000 0.0028
## [484,] -0.011618544279 0.39359184 0.0000 0.0000 0.0020
## [485,] -0.018855804139 0.78826902 0.0000 0.0000 0.0020
## [486,] -0.009757303757 0.27763284 0.0000 0.0000 0.0020
## [487,] -0.017090283849 0.49216655 0.0000 0.0000 0.0024
## [488,] 0.004925619692 0.38265231 0.0000 0.0000 0.0032
## [489,] -0.006277207751 0.26881728 0.0000 0.0000 0.0020
## [490,] -0.027915750860 0.56181334 0.0000 0.0000 0.0048
## [491,] -0.014800894443 0.50819596 0.0000 0.0000 0.0036
## [492,] -0.002319115918 0.11595580 0.0000 0.0000 0.0004
## [493,] -0.003496873201 0.32653376 0.0000 0.0000 0.0028
## [494,] 0.046835424584 1.47953993 0.0000 0.0000 0.0036
## [495,] -0.010040952447 0.32086340 0.0000 0.0000 0.0016
## [496,] -0.052951806011 1.67199012 0.0000 0.0000 0.0024
## [497,] -2.134476424506 27.89928635 0.0000 0.0000 0.0092
## [498,] 0.012077579283 0.89452195 0.0000 0.0000 0.0032
## [499,] -0.003043603448 0.18340232 0.0000 0.0000 0.0016
## [500,] 0.007856027372 1.63780425 0.0000 0.0000 0.0040
## [501,] -0.036162904540 1.26308669 0.0000 0.0000 0.0024
## [502,] -0.017105719787 0.55983922 0.0000 0.0000 0.0032
## [503,] -0.008242119569 0.30471215 0.0000 0.0000 0.0024
## [504,] -0.011749154878 0.73044559 0.0000 0.0000 0.0040
## [505,] 0.027489860471 1.49153996 0.0000 0.0000 0.0032
## [506,] -0.002752652807 1.17236117 0.0000 0.0000 0.0036
## [507,] 0.001869518856 0.22671972 0.0000 0.0000 0.0020
## [508,] -0.114474111687 3.37194109 0.0000 0.0000 0.0036
## [509,] -0.000324616770 0.66513730 0.0000 0.0000 0.0032
## [510,] -0.065670867074 1.38964905 0.0000 0.0000 0.0048
## [511,] -0.008304330869 0.33705765 0.0000 0.0000 0.0032
## [512,] -0.021027771451 0.42381202 0.0000 0.0000 0.0040
## [513,] 0.025009818260 0.88721102 0.0000 0.0000 0.0032
## [514,] -0.008749565674 0.27605469 0.0000 0.0000 0.0020
## [515,] -0.029175121261 0.98028088 0.0000 0.0000 0.0040
## [516,] -0.011105180733 1.43992925 0.0000 0.0000 0.0036
## [517,] -0.029029340105 2.03515559 0.0000 0.0000 0.0040
## [518,] 0.002121782801 0.16762617 0.0000 0.0000 0.0012
## [519,] -0.012279599003 0.48796095 0.0000 0.0000 0.0028
## [520,] -2.997726050766 32.32556987 0.0000 0.0000 0.0144
## [521,] -0.052861807069 1.80840296 0.0000 0.0000 0.0040
## [522,] 0.001908896025 0.22201078 0.0000 0.0000 0.0012
## [523,] 0.008326424483 0.86119823 0.0000 0.0000 0.0044
## [524,] -0.000696902904 0.45639412 0.0000 0.0000 0.0032
## [525,] -0.028669030127 1.03147940 0.0000 0.0000 0.0032
## [526,] -0.027864026782 1.05589509 0.0000 0.0000 0.0028
## [527,] -0.007077332746 0.35947067 0.0000 0.0000 0.0024
## [528,] -0.003165066251 0.45788826 0.0000 0.0000 0.0024
## [529,] -0.025264491998 0.73867709 0.0000 0.0000 0.0028
## [530,] -0.002407248547 0.19029916 0.0000 0.0000 0.0024
## [531,] -0.026988671900 0.79296835 0.0000 0.0000 0.0024
## [532,] -0.027904241688 0.77970081 0.0000 0.0000 0.0020
## [533,] -0.045185777690 0.90510639 0.0000 0.0000 0.0032
## [534,] -0.024288847516 0.67639589 0.0000 0.0000 0.0032
## [535,] -0.038601797467 1.82275941 0.0000 0.0000 0.0036
## [536,] -0.029216892863 0.80940221 0.0000 0.0000 0.0036
## [537,] -0.013701789131 0.40933309 0.0000 0.0000 0.0020
## [538,] 0.004075705949 0.45517398 0.0000 0.0000 0.0040
## [539,] -0.014341698543 0.96308072 0.0000 0.0000 0.0020
## [540,] -0.009575326272 0.66971146 0.0000 0.0000 0.0032
## [541,] -0.007060054628 0.28653919 0.0000 0.0000 0.0040
## [542,] -0.012043606965 0.48746361 0.0000 0.0000 0.0040
## [543,] 0.028314668300 1.78997931 0.0000 0.0000 0.0024
## [544,] 0.007813646949 0.50839276 0.0000 0.0000 0.0024
## [545,] -0.001981511014 0.33872398 0.0000 0.0000 0.0032
## [546,] -0.012736900650 1.02289589 0.0000 0.0000 0.0032
## [547,] -0.010363716157 0.52285516 0.0000 0.0000 0.0032
## [548,] -0.031452684510 0.78104597 0.0000 0.0000 0.0044
## [549,] 0.004305775664 1.36258244 0.0000 0.0000 0.0024
## [550,] -0.129130008040 2.68862453 0.0000 0.0000 0.0056
## [551,] 0.080531446342 2.55519454 0.0000 0.0000 0.0036
## [552,] -0.044850547770 0.69137476 0.0000 0.0000 0.0060
## [553,] -0.023004188346 0.73190230 0.0000 0.0000 0.0040
## [554,] -0.008586678755 0.47770567 0.0000 0.0000 0.0032
## [555,] 0.000002068235 0.07939632 0.0000 0.0000 0.0016
## [556,] -0.019235229621 1.01131797 0.0000 0.0000 0.0036
## [557,] -0.004545667809 0.14004592 0.0000 0.0000 0.0012
## [558,] -0.017375945864 0.45686944 0.0000 0.0000 0.0044
## [559,] -0.015705037547 0.32676441 0.0000 0.0000 0.0028
## [560,] -0.024787818199 0.53910394 0.0000 0.0000 0.0028
## [561,] -0.011438101184 0.72133796 0.0000 0.0000 0.0036
## [562,] -0.072383085434 1.52664383 0.0000 0.0000 0.0040
## [563,] -0.014467792585 0.69070450 0.0000 0.0000 0.0020
## [564,] -0.013353464869 0.36235357 0.0000 0.0000 0.0020
## [565,] -0.303114762368 5.43798302 0.0000 0.0000 0.0060
## [566,] 0.000726386559 0.10260490 0.0000 0.0000 0.0008
## [567,] -0.038379189583 0.98905875 0.0000 0.0000 0.0028
## [568,] -0.008404718875 0.24925761 0.0000 0.0000 0.0028
## [569,] -0.048219126132 1.39119417 0.0000 0.0000 0.0028
## [570,] -0.002457785742 0.52866129 0.0000 0.0000 0.0040
## [571,] -0.102958272408 2.38990795 0.0000 0.0000 0.0040
## [572,] -0.019193101806 1.34281231 0.0000 0.0000 0.0032
## [573,] -0.396076693746 5.78309796 0.0000 0.0000 0.0092
## [574,] -0.006313014750 0.41562784 0.0000 0.0000 0.0024
## [575,] -0.033720494551 0.94647386 0.0000 0.0000 0.0036
## [576,] -0.011152609663 0.31138895 0.0000 0.0000 0.0040
## [577,] -0.013059316532 0.61140019 0.0000 0.0000 0.0016
## [578,] -0.100127876897 2.41655345 0.0000 0.0000 0.0048
## [579,] -0.008973082135 0.39429415 0.0000 0.0000 0.0044
## [580,] -0.011030843931 0.26967397 0.0000 0.0000 0.0024
## [581,] -0.201728789034 3.27176164 0.0000 0.0000 0.0064
## [582,] -0.041803502023 1.28385285 0.0000 0.0000 0.0032
## [583,] -0.097971804684 1.67550962 0.0000 0.0000 0.0072
## [584,] -0.006987558911 0.20523184 0.0000 0.0000 0.0016
## [585,] -0.006130884904 0.30916311 0.0000 0.0000 0.0016
## [586,] -0.042517441424 1.09125098 0.0000 0.0000 0.0028
## [587,] -0.040261410417 1.49989696 0.0000 0.0000 0.0024
## [588,] -0.003070691183 0.22089697 0.0000 0.0000 0.0024
## [589,] -0.018134767918 0.60141194 0.0000 0.0000 0.0028
## [590,] -0.011828056074 0.34018718 0.0000 0.0000 0.0024
## [591,] -0.010603148848 0.36074802 0.0000 0.0000 0.0040
## [592,] -0.126385116105 3.19453967 0.0000 0.0000 0.0048
## [593,] 0.004346256392 0.29474449 0.0000 0.0000 0.0028
## [594,] 0.001607894761 0.86622374 0.0000 0.0000 0.0036
## [595,] -0.006843810579 0.27519376 0.0000 0.0000 0.0036
## [596,] -0.213985355554 3.97810615 0.0000 0.0000 0.0060
## [597,] 0.103239089171 2.44129021 0.0000 0.0000 0.0036
## [598,] -0.033178388236 1.34579511 0.0000 0.0000 0.0028
## [599,] -0.018999757210 0.48023082 0.0000 0.0000 0.0044
## [600,] -0.020688925033 0.95490308 0.0000 0.0000 0.0028
## [601,] 0.001052383986 0.17934720 0.0000 0.0000 0.0020
## [602,] -0.000543938060 0.03789731 0.0000 0.0000 0.0008
## [603,] -0.006890501416 0.23812849 0.0000 0.0000 0.0012
## [604,] -0.024701774100 0.84993751 0.0000 0.0000 0.0032
## [605,] -0.018436160595 0.50035996 0.0000 0.0000 0.0020
## [606,] -0.032711158116 0.77386803 0.0000 0.0000 0.0028
## [607,] -0.033769528409 0.93590009 0.0000 0.0000 0.0052
## [608,] 0.016533695553 0.88303353 0.0000 0.0000 0.0028
## [609,] -0.017040950331 0.72590279 0.0000 0.0000 0.0040
## [610,] -0.000075473388 0.23066715 0.0000 0.0000 0.0020
## [611,] -0.044911236588 1.00893242 0.0000 0.0000 0.0040
## [612,] -0.207377264934 6.62336792 0.0000 0.0000 0.0020
## [613,] -0.015633233961 0.36642989 0.0000 0.0000 0.0028
## [614,] -0.014466193983 0.48746437 0.0000 0.0000 0.0028
## [615,] -0.009470066567 0.19916754 0.0000 0.0000 0.0028
## [616,] -0.011145309563 0.34862780 0.0000 0.0000 0.0016
## [617,] -0.073694412234 2.01949504 0.0000 0.0000 0.0040
## [618,] -0.002270744493 0.51013186 0.0000 0.0000 0.0024
## [619,] -0.051986057943 1.76236121 0.0000 0.0000 0.0040
## [620,] 0.341216508777 4.97323382 0.0000 0.0000 0.0068
## [621,] -0.029057316208 1.20740489 0.0000 0.0000 0.0044
## [622,] -0.004170036862 0.25888583 0.0000 0.0000 0.0036
## [623,] -0.016762095999 0.40390086 0.0000 0.0000 0.0044
## [624,] -0.008841936632 0.55027973 0.0000 0.0000 0.0020
## [625,] -0.039895625749 0.86854427 0.0000 0.0000 0.0036
## [626,] -0.020756836968 0.44238837 0.0000 0.0000 0.0032
## [627,] -0.091342617027 2.25213631 0.0000 0.0000 0.0052
## [628,] -0.021496827341 0.52338538 0.0000 0.0000 0.0044
## [629,] -0.031196556951 0.81346827 0.0000 0.0000 0.0040
## [630,] -0.009783985344 0.46546275 0.0000 0.0000 0.0040
## [631,] -0.004560723218 0.23887607 0.0000 0.0000 0.0016
## [632,] 0.022300146074 1.50436254 0.0000 0.0000 0.0012
## [633,] -0.032713580312 0.92275375 0.0000 0.0000 0.0028
## [634,] -0.071150894745 1.35655854 0.0000 0.0000 0.0052
## [635,] 0.038541260512 3.00516041 0.0000 0.0000 0.0040
## [636,] -0.007490317427 0.28593387 0.0000 0.0000 0.0032
## [637,] -0.008985082498 0.31613161 0.0000 0.0000 0.0020
## [638,] -0.006528229600 0.37584409 0.0000 0.0000 0.0032
## [639,] 0.005332243328 1.28345259 0.0000 0.0000 0.0036
## [640,] -0.013339265053 0.54098719 0.0000 0.0000 0.0024
## [641,] 0.007569581779 0.41217586 0.0000 0.0000 0.0036
## [642,] -0.364544301470 5.57496331 0.0000 0.0000 0.0088
## [643,] 0.804756106851 9.42468385 0.0000 0.0000 0.0120
## [644,] -0.036964913415 1.46315369 0.0000 0.0000 0.0032
## [645,] -0.000739854426 0.04456326 0.0000 0.0000 0.0012
## [646,] -0.007641471135 0.35127714 0.0000 0.0000 0.0032
## [647,] -0.020616237369 0.80490443 0.0000 0.0000 0.0048
## [648,] -0.050242804962 1.30316383 0.0000 0.0000 0.0036
## [649,] -0.008910899720 0.32236444 0.0000 0.0000 0.0032
## [650,] -0.035852563233 0.83401858 0.0000 0.0000 0.00363.4.4 Predict fitted values for each individual
pred.npb3 <- predict(fit.npb3)
fittedvals3 <- pred.npb3$fitted.vals3.4.5 Plot predicted outcomes against “measured” outcomes
plot(fittedvals3, Y)
abline(a = 0, b = 1, col = "red")
3.5 Fit the NPB model without ozone and without temperature
Only ozone shows up in the NPB model. However, there is some speculation that ozone is just a proxy for some of the other variables. Here I am running the NPB model without ozone or temperature just to see if something else pops up instead.
priors.npb <- priors.npb.24
#' Exposures
colnames(X.scaled)## [1] "mean_pm" "mean_o3" "mean_temp"
## [4] "pct_tree_cover" "pct_impervious" "mean_aadt_intensity"
## [7] "dist_m_tri" "dist_m_npl" "dist_m_waste_site"
## [10] "dist_m_major_emit" "dist_m_cafo" "dist_m_mine_well"
## [13] "cvd_rate_adj" "res_rate_adj" "violent_crime_rate"
## [16] "property_crime_rate" "pct_less_hs" "pct_unemp"
## [19] "pct_limited_eng" "pct_hh_pov" "pct_poc"#' Covariates
colnames(W.scaled2)## [1] "lat" "lon" "lat_lon_int" "ed_no_hs"
## [5] "ed_hs" "ed_aa" "ed_4yr" "low_bmi"
## [9] "ovwt_bmi" "obese_bmi" "concep_spring" "concep_summer"
## [13] "concep_fall" "concep_2010" "concep_2011" "concep_2012"
## [17] "concep_2013" "maternal_age" "any_smoker" "smokeSH"
## [21] "mean_cpss" "mean_epsd" "male"# fit.npb4 <- npb(niter = 5000, nburn = 2500, X = X.scaled[,-c(2,3)], Y = Y, W = W.scaled2,
# scaleY = TRUE,
# priors = priors.npb, interact = TRUE, XWinteract = TRUE)
# save(fit.npb4, file = here::here("Results", "NPB_Birth_Weight_v4a.4.rdata"))
load(here::here("Results", "NPB_Birth_Weight_v4a.4.rdata"))
npb.sum4 <- summary(fit.npb4)3.5.1 First, main effect regression coefficients with PIPs
rownames(npb.sum4$main.effects) <- colnames(X.scaled[,-c(2,3)])
npb.sum4$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## mean_pm 0.01740483 6.666825 -13.66354 16.261833 0.2588
## pct_tree_cover -0.42808738 6.557343 -16.07193 14.870785 0.2664
## pct_impervious -2.98242948 8.784403 -29.50467 8.315785 0.3316
## mean_aadt_intensity -0.33582811 5.719151 -12.95181 13.143332 0.2432
## dist_m_tri -0.32784261 6.267080 -15.15440 14.480333 0.2580
## dist_m_npl 0.32661062 6.933992 -13.35060 18.758868 0.2620
## dist_m_waste_site 1.74392766 8.859841 -10.75379 29.415047 0.2868
## dist_m_major_emit -0.09948045 5.647990 -12.23102 13.491529 0.2452
## dist_m_cafo -3.47107470 17.884937 -52.96240 17.467822 0.3368
## dist_m_mine_well -2.78266572 9.539020 -30.03867 10.711788 0.3192
## cvd_rate_adj -3.05062600 9.576883 -30.91481 9.044841 0.3148
## res_rate_adj -2.30442258 8.327439 -24.91180 8.452087 0.3104
## violent_crime_rate -0.21414248 6.094327 -13.88438 13.958877 0.2600
## property_crime_rate -1.18082454 6.079274 -17.81515 10.538959 0.2608
## pct_less_hs -1.68535722 8.358050 -22.33047 12.282048 0.2988
## pct_unemp -21.61340643 27.288321 -85.60404 0.000000 0.6404
## pct_limited_eng -1.54816907 7.169160 -21.28668 11.274985 0.3024
## pct_hh_pov -0.82644993 7.254424 -16.95409 13.457831 0.2788
## pct_poc -1.26695546 8.277818 -21.24654 13.978007 0.29763.5.2 Next, posterior means and CIs for covariates
rownames(npb.sum4$covariates)[2:nrow(npb.sum4$covariates)] <- colnames(W.scaled2)
npb.sum4$covariates## Posterior Mean SD 95% CI Lower 95% CI Upper
## <NA> 3082.964159 218.31444 2666.165179 3496.98883
## lat -9.514005 325.52873 -657.187948 635.18284
## lon 12.764785 155.28519 -294.162668 318.36380
## lat_lon_int 1.435636 394.32695 -788.038926 775.75827
## ed_no_hs 111.713087 77.30533 -41.633044 265.05261
## ed_hs 66.647739 70.85823 -70.204042 205.63410
## ed_aa 15.575205 60.57621 -103.141967 133.62891
## ed_4yr 59.803128 52.88785 -42.903199 165.34836
## low_bmi -105.463024 94.74011 -288.888479 76.96030
## ovwt_bmi 31.081805 41.20973 -47.859949 112.26486
## obese_bmi 99.227241 47.07821 4.635381 192.13086
## concep_spring -38.795879 49.07741 -136.048470 55.15986
## concep_summer 65.600579 49.62205 -30.973515 164.08209
## concep_fall 68.940271 47.98050 -26.548434 163.50593
## concep_2010 -4.802284 216.03491 -424.271817 408.52731
## concep_2011 -24.535652 215.19071 -434.143224 384.80841
## concep_2012 -54.791861 214.74605 -468.629692 366.34955
## concep_2013 67.670824 215.49603 -345.352147 478.39258
## maternal_age 81.054147 22.47691 36.460698 124.78256
## any_smoker -146.697446 64.40336 -270.919548 -20.62775
## smokeSH -114.234422 45.04711 -202.917718 -29.30478
## mean_cpss 12.594717 20.40150 -27.405490 51.69029
## mean_epsd -53.324959 20.66938 -93.707931 -13.08126
## male 157.246918 34.33731 89.717584 222.695473.5.3 Interactions
Next, all of the interactions between exposures or between exposures and covariates
npb.sum4$interactions## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] -0.0535398565 0.8554814 0 0 0.0124
## [2,] -0.0277599988 0.5874716 0 0 0.0104
## [3,] 0.0255571941 1.1632129 0 0 0.0124
## [4,] -0.0357963402 0.8616498 0 0 0.0128
## [5,] -0.0355543254 0.6103949 0 0 0.0104
## [6,] -0.0688209405 1.3881109 0 0 0.0116
## [7,] -0.0445171591 0.6889427 0 0 0.0104
## [8,] -0.1378766561 1.7597244 0 0 0.0176
## [9,] -0.0289782465 0.6063844 0 0 0.0108
## [10,] -0.0336587894 1.0159475 0 0 0.0132
## [11,] -0.0233540581 0.4725086 0 0 0.0096
## [12,] -0.0494650615 0.7213515 0 0 0.0124
## [13,] -0.0454922259 0.8267308 0 0 0.0120
## [14,] -0.0740927258 1.1672629 0 0 0.0116
## [15,] -0.0385564524 0.5806577 0 0 0.0096
## [16,] -0.0820598624 1.0611379 0 0 0.0180
## [17,] -0.0061676447 0.3968900 0 0 0.0088
## [18,] -0.0252153623 0.9371627 0 0 0.0152
## [19,] 0.0281696484 0.8763174 0 0 0.0104
## [20,] -0.0081305603 0.8165736 0 0 0.0112
## [21,] 0.0012292995 0.7253463 0 0 0.0148
## [22,] -0.0920894663 1.2864090 0 0 0.0168
## [23,] -0.0042069433 0.6677543 0 0 0.0112
## [24,] 0.0377529265 0.9537081 0 0 0.0088
## [25,] -0.0302423366 0.5688879 0 0 0.0108
## [26,] -0.0750717333 1.2152646 0 0 0.0144
## [27,] 0.0071106223 0.7592570 0 0 0.0092
## [28,] -0.0147856077 0.8315756 0 0 0.0108
## [29,] -0.0277397628 0.6986635 0 0 0.0096
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## [354,] -0.0252662461 0.5031216 0 0 0.0120
## [355,] -0.0047883097 1.0391818 0 0 0.0172
## [356,] 0.0022405328 0.6223445 0 0 0.0092
## [357,] 0.0048555457 0.7321943 0 0 0.0100
## [358,] -0.0301534320 1.0456127 0 0 0.0132
## [359,] 0.0782300797 2.9092308 0 0 0.0112
## [360,] -0.0941389368 1.7878229 0 0 0.0164
## [361,] -0.0163216579 0.6968084 0 0 0.0108
## [362,] -0.0587139234 0.9708574 0 0 0.0124
## [363,] -0.1395803037 3.3610443 0 0 0.0116
## [364,] -0.0406331318 1.8686695 0 0 0.0172
## [365,] -0.0267283241 0.7827867 0 0 0.0128
## [366,] -0.0699290075 1.2529449 0 0 0.0144
## [367,] -0.0114237773 0.6008901 0 0 0.0108
## [368,] 0.0446564944 1.8279960 0 0 0.0136
## [369,] -0.0029104968 1.9623826 0 0 0.0140
## [370,] 0.0851744271 2.8007365 0 0 0.0100
## [371,] -0.0773573571 1.3458747 0 0 0.0156
## [372,] -0.0629260725 1.2682154 0 0 0.0144
## [373,] -0.0164903318 0.6054618 0 0 0.0184
## [374,] -0.1846699042 5.7855249 0 0 0.0172
## [375,] -0.0938309275 1.8117557 0 0 0.0132
## [376,] -0.0314303452 0.6162595 0 0 0.0092
## [377,] -0.0221551492 0.5309392 0 0 0.0112
## [378,] -0.0827136214 1.4309522 0 0 0.0164
## [379,] 0.0335127316 1.1778972 0 0 0.0108
## [380,] 0.0233813409 1.1260255 0 0 0.0148
## [381,] -0.0484931523 0.9830387 0 0 0.0116
## [382,] -0.0199669857 1.0938196 0 0 0.0120
## [383,] -0.0775153575 1.2548619 0 0 0.0132
## [384,] -0.0121156745 1.1218298 0 0 0.0144
## [385,] 0.0179515081 0.7787999 0 0 0.0144
## [386,] -0.1357247010 3.1202231 0 0 0.0136
## [387,] -0.0368310721 0.8046809 0 0 0.0104
## [388,] -0.0257300141 0.7500180 0 0 0.0148
## [389,] -0.0238558322 1.0594992 0 0 0.0144
## [390,] -0.1349818732 2.2564102 0 0 0.0176
## [391,] -0.0069666122 1.3060318 0 0 0.0140
## [392,] -0.0215410619 0.8868134 0 0 0.0108
## [393,] 0.0995894170 2.0930555 0 0 0.0132
## [394,] -1.1714819237 10.4477363 0 0 0.0240
## [395,] -0.0311524954 0.5946701 0 0 0.0096
## [396,] -0.0176219728 0.8045246 0 0 0.0112
## [397,] -0.0120140792 0.6400092 0 0 0.0096
## [398,] -0.0496533167 0.9123524 0 0 0.0140
## [399,] 0.0102881505 0.8829526 0 0 0.0128
## [400,] -0.0006675648 0.5233028 0 0 0.0108
## [401,] -0.0985334889 1.6598146 0 0 0.0128
## [402,] -0.0244185339 0.6695409 0 0 0.0092
## [403,] -0.0403133383 0.7566425 0 0 0.0100
## [404,] -0.0297759989 0.4725258 0 0 0.0096
## [405,] -0.1134107912 2.2823800 0 0 0.0144
## [406,] -0.0766191975 2.0847773 0 0 0.0132
## [407,] -0.0347050479 0.7122233 0 0 0.0120
## [408,] -0.1810995916 3.0366084 0 0 0.0192
## [409,] -0.0555759544 1.4045868 0 0 0.0112
## [410,] -0.0306577138 0.9934268 0 0 0.0132
## [411,] -0.0127761897 1.2176525 0 0 0.0112
## [412,] -0.0439581904 0.9275935 0 0 0.0088
## [413,] -0.0517067746 1.0478064 0 0 0.0164
## [414,] -0.1478757742 2.4749427 0 0 0.0136
## [415,] -0.0885330640 1.6671236 0 0 0.0140
## [416,] -0.1007692644 1.3503364 0 0 0.0180
## [417,] 0.3287193528 4.8175565 0 0 0.0172
## [418,] -0.0491135236 0.6689021 0 0 0.0128
## [419,] -0.0085869778 0.5587601 0 0 0.0080
## [420,] -0.0954179125 1.5290524 0 0 0.0128
## [421,] -0.0337360837 0.8448320 0 0 0.0148
## [422,] -0.0273252074 0.5335315 0 0 0.0120
## [423,] -0.0190790470 0.7921363 0 0 0.0112
## [424,] -0.0553627189 0.9803798 0 0 0.0152
## [425,] -0.0495417451 1.5055328 0 0 0.0124
## [426,] -0.0291552692 0.7651675 0 0 0.0132
## [427,] -0.0309927087 0.6889990 0 0 0.0144
## [428,] -0.0385158566 0.6403777 0 0 0.0144
## [429,] -0.0160177130 0.8299958 0 0 0.0128
## [430,] -0.0259135005 0.7854044 0 0 0.0116
## [431,] -0.1820848454 2.8136124 0 0 0.0168
## [432,] -0.1356626636 3.1914046 0 0 0.0156
## [433,] -0.0041779944 1.0952521 0 0 0.0128
## [434,] -0.0323654519 0.5779149 0 0 0.0092
## [435,] -0.0591659080 1.2820509 0 0 0.0104
## [436,] -0.0025565029 0.9469463 0 0 0.0152
## [437,] -0.0729572413 1.0439326 0 0 0.0184
## [438,] -0.1297239181 2.3323048 0 0 0.0152
## [439,] -0.0658152462 1.2009247 0 0 0.0108
## [440,] 0.1347551550 2.7653624 0 0 0.0148
## [441,] -0.0421663180 0.7411528 0 0 0.0112
## [442,] 0.0084089201 0.7559332 0 0 0.0136
## [443,] -0.1130573559 2.2377182 0 0 0.0140
## [444,] -0.0352913258 0.8514778 0 0 0.0112
## [445,] -0.0101461515 0.4857774 0 0 0.0112
## [446,] -0.0224797526 0.8747943 0 0 0.0120
## [447,] -0.0548945762 1.3985419 0 0 0.0108
## [448,] -0.0483941876 0.9678491 0 0 0.0148
## [449,] -0.0389438185 0.7818459 0 0 0.0136
## [450,] -0.0304748501 0.5744277 0 0 0.0124
## [451,] -0.0563976487 0.8879204 0 0 0.0172
## [452,] -0.0012804096 0.8564892 0 0 0.0132
## [453,] -0.0119999067 0.7183194 0 0 0.0140
## [454,] -0.0741645113 1.4937353 0 0 0.0120
## [455,] -0.4454253112 10.5309020 0 0 0.0188
## [456,] -0.0606741732 2.0292095 0 0 0.0112
## [457,] 0.0311903860 1.4087364 0 0 0.0108
## [458,] -0.0150267528 0.7463461 0 0 0.0104
## [459,] 0.0089377035 0.8801013 0 0 0.0140
## [460,] -0.0239324365 0.6449306 0 0 0.0116
## [461,] -0.0409116413 1.4992657 0 0 0.0160
## [462,] -0.0510436686 0.7730598 0 0 0.0128
## [463,] 0.0456263225 1.8046072 0 0 0.0152
## [464,] -0.0053270123 0.7762664 0 0 0.0120
## [465,] -0.0089377960 1.0687123 0 0 0.0116
## [466,] -0.0698618894 1.8185994 0 0 0.0128
## [467,] 0.0044727925 0.7532355 0 0 0.0104
## [468,] -0.1574219545 2.4578308 0 0 0.0172
## [469,] -0.0528057283 0.9004905 0 0 0.0152
## [470,] -0.0519656288 0.8886719 0 0 0.0136
## [471,] -0.0326272174 1.1316875 0 0 0.0092
## [472,] -0.0097075499 0.5883777 0 0 0.0136
## [473,] -0.0041254381 0.6858135 0 0 0.0124
## [474,] -0.0144803501 0.6596757 0 0 0.0076
## [475,] -0.0281200664 0.9066350 0 0 0.0104
## [476,] -0.0235500929 1.0726064 0 0 0.0116
## [477,] -0.0355699628 1.0010247 0 0 0.0120
## [478,] -0.3199229738 8.1957864 0 0 0.0152
## [479,] -0.0712927583 1.4738917 0 0 0.0116
## [480,] 0.0047483816 0.8533652 0 0 0.0104
## [481,] -0.0157251729 0.6220371 0 0 0.0088
## [482,] -0.0315544937 0.7884933 0 0 0.0112
## [483,] -0.1025589032 2.3039044 0 0 0.0120
## [484,] -0.0520991204 1.7932099 0 0 0.0116
## [485,] -0.0252776714 1.1420361 0 0 0.0160
## [486,] -0.0223240688 1.0785619 0 0 0.0132
## [487,] -0.0502296836 1.2151220 0 0 0.0084
## [488,] -0.0068791980 0.6631706 0 0 0.0152
## [489,] -0.0543707585 0.9019724 0 0 0.0112
## [490,] -0.0149060875 0.6401027 0 0 0.0132
## [491,] -0.1196036458 2.0826305 0 0 0.0176
## [492,] -0.0303435198 0.8253081 0 0 0.0096
## [493,] -0.0134987247 0.7442187 0 0 0.0112
## [494,] -0.0263858828 0.5475027 0 0 0.0072
## [495,] -0.1139105649 1.8465774 0 0 0.0164
## [496,] -0.0345007499 0.6768059 0 0 0.0140
## [497,] -0.0215312032 2.9983844 0 0 0.0164
## [498,] -0.0169193440 1.4698842 0 0 0.0124
## [499,] -0.0503516377 1.3143852 0 0 0.0152
## [500,] -0.0702099796 2.0673410 0 0 0.0120
## [501,] -0.0793586130 1.7850180 0 0 0.0136
## [502,] -0.0045875219 0.5393403 0 0 0.0104
## [503,] -0.0284422397 0.9856570 0 0 0.0112
## [504,] -0.0579015665 1.5494622 0 0 0.0108
## [505,] 0.0001927488 1.0962692 0 0 0.0116
## [506,] -0.0562989899 1.2854899 0 0 0.0116
## [507,] -0.0101133980 1.0184602 0 0 0.0128
## [508,] -0.1706100548 2.6925370 0 0 0.0176
## [509,] 0.0487431949 1.6508168 0 0 0.0128
## [510,] -0.1388462448 2.5711944 0 0 0.0180
## [511,] -0.0352051982 0.6776727 0 0 0.0116
## [512,] -0.0354814760 1.0049941 0 0 0.0124
## [513,] 0.0227524025 1.1172539 0 0 0.0132
## [514,] -0.0218979384 0.4156544 0 0 0.0088
## [515,] 0.0011531605 0.5217240 0 0 0.0092
## [516,] -0.0434169327 0.7402442 0 0 0.0148
## [517,] -0.0295150253 1.1993905 0 0 0.0172
## [518,] -0.1227369855 1.7160016 0 0 0.0164
## [519,] -0.0399775866 0.7252686 0 0 0.0124
## [520,] -0.1621839842 2.9586232 0 0 0.0168
## [521,] -0.0239417136 0.7770905 0 0 0.0152
## [522,] -0.0841600467 1.7071529 0 0 0.0148
## [523,] -0.3316423080 4.1672280 0 0 0.0160
## [524,] -0.0594682333 1.4186603 0 0 0.0180
## [525,] -0.1338299417 2.4915369 0 0 0.0152
## [526,] -0.0387584337 0.8415752 0 0 0.0152
## [527,] -0.0592852799 1.2188360 0 0 0.0144
## [528,] -0.0342811977 0.7509679 0 0 0.0176
## [529,] -0.3902011787 5.0841336 0 0 0.0192
## [530,] -0.0603723117 0.9080311 0 0 0.0120
## [531,] -0.3785734122 4.9994501 0 0 0.0172
## [532,] -0.0018561321 0.7034875 0 0 0.0116
## [533,] -0.0436524285 1.2053423 0 0 0.0120
## [534,] -0.0413731049 0.7968729 0 0 0.0120
## [535,] -0.1676153514 3.8199016 0 0 0.0156
## [536,] -0.1875010569 3.1558497 0 0 0.0144
## [537,] -0.0521748161 0.9359901 0 0 0.0104
## [538,] -0.0180576172 0.5358664 0 0 0.0140
## [539,] -0.8309176440 7.8545148 0 0 0.0292
## [540,] -0.1404784561 2.4221056 0 0 0.0148
## [541,] -0.2670581529 3.3141116 0 0 0.0192
## [542,] -0.0530849319 0.7421441 0 0 0.0116
## [543,] -0.0565601953 1.1184321 0 0 0.0152
## [544,] 0.0096006952 0.8199066 0 0 0.0092
## [545,] -0.1448135955 2.5292983 0 0 0.0168
## [546,] -0.0604285155 1.6669877 0 0 0.0128
## [547,] -0.0307996786 1.2351688 0 0 0.0144
## [548,] -0.0169982953 0.6369654 0 0 0.0112
## [549,] 0.0042088282 0.9711590 0 0 0.0104
## [550,] -0.1058490803 1.5195280 0 0 0.0140
## [551,] -0.0237602173 0.7940822 0 0 0.0116
## [552,] -0.0253231444 1.8885887 0 0 0.0132
## [553,] -0.0154763632 0.7991267 0 0 0.0120
## [554,] -0.1589847457 1.8586019 0 0 0.0204
## [555,] 0.0158796288 1.0103572 0 0 0.0136
## [556,] -0.1025583126 2.5698655 0 0 0.0128
## [557,] -0.0071940594 0.4700438 0 0 0.0104
## [558,] -0.0543211723 1.6323820 0 0 0.0136
## [559,] -0.0163938623 0.9459970 0 0 0.0108
## [560,] -0.0323444499 0.5378742 0 0 0.0084
## [561,] -0.0239963840 0.8501048 0 0 0.0128
## [562,] -0.0333813087 0.9014754 0 0 0.0100
## [563,] -0.0012151227 0.8015779 0 0 0.0096
## [564,] -0.1421990748 2.2553920 0 0 0.0156
## [565,] -0.0928661966 1.4907297 0 0 0.0168
## [566,] 0.0011348669 1.0296102 0 0 0.0092
## [567,] 0.0101763584 1.0693678 0 0 0.0152
## [568,] -0.0586740331 1.1111645 0 0 0.0132
## [569,] -0.0684125029 1.2679190 0 0 0.0108
## [570,] -0.1171469421 2.1579338 0 0 0.0120
## [571,] -0.0273887135 0.5841025 0 0 0.0080
## [572,] 0.0026318322 1.0076667 0 0 0.0092
## [573,] -0.0426927657 0.7401675 0 0 0.0128
## [574,] -0.0038601525 0.8015268 0 0 0.0124
## [575,] -0.0960533659 1.7560535 0 0 0.0136
## [576,] -0.0467252421 1.1956374 0 0 0.0132
## [577,] -0.0635958162 1.5575722 0 0 0.0096
## [578,] 0.2653361117 4.2502310 0 0 0.0164
## [579,] -0.1001262265 2.4042200 0 0 0.0120
## [580,] -0.0298604533 1.0531657 0 0 0.0140
## [581,] -0.1457337210 2.9160920 0 0 0.0116
## [582,] 0.0151159682 1.3015951 0 0 0.0096
## [583,] -0.0531626298 0.6824881 0 0 0.0136
## [584,] -0.0238795571 0.8771228 0 0 0.0124
## [585,] -0.0805775292 1.3170263 0 0 0.0156
## [586,] -0.0352694022 0.7153470 0 0 0.0140
## [587,] -0.1278110778 1.4612132 0 0 0.0164
## [588,] -0.0585217288 1.3671481 0 0 0.0100
## [589,] -0.0537305557 1.2121609 0 0 0.0132
## [590,] 0.0497467631 2.0005320 0 0 0.0100
## [591,] -0.0364791537 0.9034047 0 0 0.0164
## [592,] -0.1214194993 2.0566505 0 0 0.0180
## [593,] -0.1129100161 2.5673314 0 0 0.0164
## [594,] -0.0167547914 0.4065176 0 0 0.0112
## [595,] -0.0600656663 2.2413575 0 0 0.0136
## [596,] -0.0731911175 1.7236169 0 0 0.0124
## [597,] -0.0022971184 0.9686253 0 0 0.0128
## [598,] -0.1751888479 3.4273102 0 0 0.0156
## [599,] -0.0276795540 0.8566947 0 0 0.0112
## [600,] -0.4735701251 6.5896271 0 0 0.0200
## [601,] 0.4192674309 5.9960167 0 0 0.0180
## [602,] -0.0787735480 1.7553057 0 0 0.0132
## [603,] -0.0332669479 0.8107603 0 0 0.0100
## [604,] -0.0831124467 2.2230469 0 0 0.0152
## [605,] -0.0062627532 0.8298027 0 0 0.0096
## [606,] -0.0782849945 1.2650414 0 0 0.0112
## [607,] -0.0560609597 0.7830587 0 0 0.0148
## [608,] -0.0234426753 0.6803685 0 0 0.01163.5.4 Predict fitted values for each individual
pred.npb4 <- predict(fit.npb4)
fittedvals4 <- pred.npb4$fitted.vals3.5.5 Plot predicted outcomes against “measured” outcomes
plot(fittedvals4, Y)
abline(a = 0, b = 1, col = "red")
4 Linear models for each predictor
4.1 Screening the exposures
Here I’m going to loop through some linear regression models to see if anything shows up here. Remember that the exposure and covariates have all been scaled.
The standard deviation of the mean_o3 variable is 3.06 ppb
lm_results <- data.frame()
for(i in 1:length(colnames(X.scaled))) {
lm_df <- as.data.frame(cbind(Y, X.scaled[,i], W.scaled2))
names(lm_df)[2] <- colnames(X.scaled)[i]
ad_lm <- lm(birth_weight ~ ., data = lm_df)
temp <- data.frame(exp = colnames(X.scaled)[i],
beta = summary(ad_lm)$coefficients[2,1],
beta.se = summary(ad_lm)$coefficients[2,2],
p.value = summary(ad_lm)$coefficients[2,4])
temp$lcl <- temp$beta - 1.96*temp$beta.se
temp$ucl <- temp$beta + 1.96*temp$beta.se
lm_results <- bind_rows(lm_results, temp)
rm(temp)
}
lm_resultswrite_csv(lm_results, here::here("Results", "LM_Effects_Birth_Weight_v4a.csv"))5 Linear model with the ozone predictor
The GAM model indicates a non-linear relationship between O3 and birth weight, None of the other exposures had a PIP > 0.5. Remember that the exposure and covariates have all been scaled.
The standard deviation of the mean_o3 variable is 3.06 ppb
lm_df <- as.data.frame(cbind(Y, X.scaled[, "mean_o3"], W.scaled2))
names(lm_df)## [1] "birth_weight" "V2" "lat" "lon"
## [5] "lat_lon_int" "ed_no_hs" "ed_hs" "ed_aa"
## [9] "ed_4yr" "low_bmi" "ovwt_bmi" "obese_bmi"
## [13] "concep_spring" "concep_summer" "concep_fall" "concep_2010"
## [17] "concep_2011" "concep_2012" "concep_2013" "maternal_age"
## [21] "any_smoker" "smokeSH" "mean_cpss" "mean_epsd"
## [25] "male"names(lm_df)[2] <- "mean_o3"
head(lm_df)bw_lm <- lm(birth_weight ~ mean_o3 +
lat + lon + lat_lon_int +
ed_no_hs + ed_hs + ed_aa + ed_4yr +
low_bmi + ovwt_bmi + obese_bmi +
concep_spring + concep_summer + concep_fall +
concep_2010 + concep_2011 + concep_2012 + concep_2013 +
maternal_age + any_smoker + smokeSH +
mean_cpss + mean_epsd + male,
data = lm_df)
summary(bw_lm)##
## Call:
## lm(formula = birth_weight ~ mean_o3 + lat + lon + lat_lon_int +
## ed_no_hs + ed_hs + ed_aa + ed_4yr + low_bmi + ovwt_bmi +
## obese_bmi + concep_spring + concep_summer + concep_fall +
## concep_2010 + concep_2011 + concep_2012 + concep_2013 + maternal_age +
## any_smoker + smokeSH + mean_cpss + mean_epsd + male, data = lm_df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2526.7 -284.1 24.1 302.9 1398.8
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2943.870 513.522 5.733 0.0000000136 ***
## mean_o3 -41.376 32.327 -1.280 0.200906
## lat -8863.787 18294.703 -0.485 0.628153
## lon 4193.179 8614.217 0.487 0.626541
## lat_lon_int -10699.714 22102.744 -0.484 0.628444
## ed_no_hs 95.919 75.713 1.267 0.205539
## ed_hs 55.210 67.762 0.815 0.415426
## ed_aa 6.485 60.194 0.108 0.914235
## ed_4yr 62.036 52.894 1.173 0.241182
## low_bmi -117.337 96.223 -1.219 0.223013
## ovwt_bmi 26.567 41.682 0.637 0.524043
## obese_bmi 91.531 47.151 1.941 0.052549 .
## concep_spring -56.525 51.855 -1.090 0.275989
## concep_summer -10.173 77.992 -0.130 0.896247
## concep_fall -1.152 73.171 -0.016 0.987438
## concep_2010 179.841 514.475 0.350 0.726752
## concep_2011 167.151 515.409 0.324 0.745783
## concep_2012 151.366 516.497 0.293 0.769544
## concep_2013 241.588 514.683 0.469 0.638906
## maternal_age 82.970 22.667 3.660 0.000267 ***
## any_smoker -145.355 65.805 -2.209 0.027442 *
## smokeSH -116.630 45.606 -2.557 0.010716 *
## mean_cpss 17.819 20.494 0.870 0.384812
## mean_epsd -56.755 20.875 -2.719 0.006681 **
## male 155.755 33.780 4.611 0.0000046091 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 500.4 on 872 degrees of freedom
## Multiple R-squared: 0.1212, Adjusted R-squared: 0.09697
## F-statistic: 5.009 on 24 and 872 DF, p-value: 0.000000000000111plot(bw_lm)## Warning: not plotting observations with leverage one:
## 1
6 Try a GAM with the ozone predictor
The NPB model above indicates that there might be a signal for ozone. None of the other exposures had a PIP > 0.5. Here I’ve got a GAM with a smoothing term for ozone to see about potential nonlinear effects
library(mgcv)## Loading required package: nlme##
## Attaching package: 'nlme'## The following object is masked from 'package:dplyr':
##
## collapse## This is mgcv 1.8-33. For overview type 'help("mgcv-package")'.gam_df <- as.data.frame(cbind(Y, X.scaled[, "mean_o3"], W.scaled2))
names(gam_df)## [1] "birth_weight" "V2" "lat" "lon"
## [5] "lat_lon_int" "ed_no_hs" "ed_hs" "ed_aa"
## [9] "ed_4yr" "low_bmi" "ovwt_bmi" "obese_bmi"
## [13] "concep_spring" "concep_summer" "concep_fall" "concep_2010"
## [17] "concep_2011" "concep_2012" "concep_2013" "maternal_age"
## [21] "any_smoker" "smokeSH" "mean_cpss" "mean_epsd"
## [25] "male"names(gam_df)[2] <- "mean_o3"
head(gam_df)bw_gam <- gam(birth_weight ~ s(mean_o3) +
lat + lon + lat_lon_int +
ed_no_hs + ed_hs + ed_aa + ed_4yr +
low_bmi + ovwt_bmi + obese_bmi +
concep_spring + concep_summer + concep_fall +
concep_2010 + concep_2011 + concep_2012 + concep_2013 +
maternal_age + any_smoker + smokeSH +
mean_cpss + mean_epsd + male,
data = gam_df, method = "REML")
summary(bw_gam)##
## Family: gaussian
## Link function: identity
##
## Formula:
## birth_weight ~ s(mean_o3) + lat + lon + lat_lon_int + ed_no_hs +
## ed_hs + ed_aa + ed_4yr + low_bmi + ovwt_bmi + obese_bmi +
## concep_spring + concep_summer + concep_fall + concep_2010 +
## concep_2011 + concep_2012 + concep_2013 + maternal_age +
## any_smoker + smokeSH + mean_cpss + mean_epsd + male
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2827.561 492.252 5.744 0.0000000128 ***
## lat -3008.080 17567.633 -0.171 0.86408
## lon 1417.332 8271.976 0.171 0.86400
## lat_lon_int -3631.528 21224.308 -0.171 0.86418
## ed_no_hs 77.975 72.619 1.074 0.28323
## ed_hs 50.882 65.075 0.782 0.43448
## ed_aa 3.171 57.668 0.055 0.95616
## ed_4yr 67.378 50.758 1.327 0.18471
## low_bmi -124.418 92.523 -1.345 0.17907
## ovwt_bmi 36.084 39.951 0.903 0.36667
## obese_bmi 104.702 45.303 2.311 0.02106 *
## concep_spring -97.282 54.276 -1.792 0.07343 .
## concep_summer -23.544 80.533 -0.292 0.77009
## concep_fall -4.147 74.978 -0.055 0.95590
## concep_2010 278.719 493.857 0.564 0.57265
## concep_2011 249.234 494.894 0.504 0.61466
## concep_2012 298.096 496.001 0.601 0.54800
## concep_2013 394.229 494.471 0.797 0.42551
## maternal_age 68.907 21.776 3.164 0.00161 **
## any_smoker -168.378 63.215 -2.664 0.00787 **
## smokeSH -87.319 43.856 -1.991 0.04679 *
## mean_cpss 14.225 19.635 0.724 0.46897
## mean_epsd -55.145 20.020 -2.755 0.00600 **
## male 160.637 32.393 4.959 0.0000008526 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(mean_o3) 5.869 7.123 11.62 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.174 Deviance explained = 20%
## -REML = 6681.3 Scale est. = 2.2912e+05 n = 897jpeg(here::here("Figs", "Ozone_GAM_Birth_Weight_v4a.jpeg"))
plot(bw_gam, main = "GAM with a smoothing term for ozone",
xlab = "Ozone (scaled)", ylab = "Change in birth weight (g)")
dev.off()## quartz_off_screen
## 27 GAM Sensitivity Analysis
The previous GAM suggested a possible nonlinear relationship between ozone and birth weight. However, this might be the influence of abnormally high and low exposures.
Therefore, Ander suggested a sensitivity analysis where we excluded the top and bottom 2.5% of data and just use the middle 95%.
library(mgcv)
quantile(X.scaled[,"mean_o3"], probs = c(0.025, 0.975))## 2.5% 97.5%
## -1.703410 1.852552q_2.5 <- quantile(X.scaled[,"mean_o3"], probs = c(0.025))
q_97.5 <- quantile(X.scaled[,"mean_o3"], probs = c(0.975))
gam_df <- as.data.frame(cbind(Y, X.scaled[, "mean_o3"], W.scaled2))
names(gam_df)## [1] "birth_weight" "V2" "lat" "lon"
## [5] "lat_lon_int" "ed_no_hs" "ed_hs" "ed_aa"
## [9] "ed_4yr" "low_bmi" "ovwt_bmi" "obese_bmi"
## [13] "concep_spring" "concep_summer" "concep_fall" "concep_2010"
## [17] "concep_2011" "concep_2012" "concep_2013" "maternal_age"
## [21] "any_smoker" "smokeSH" "mean_cpss" "mean_epsd"
## [25] "male"names(gam_df)[2] <- "mean_o3"
head(gam_df)gam_df2 <- gam_df %>%
filter(mean_o3 > q_2.5 & mean_o3 < q_97.5)
hist(gam_df2$mean_o3)
bw_gam2 <- gam(birth_weight ~ s(mean_o3) +
lat + lon + lat_lon_int +
ed_no_hs + ed_hs + ed_aa + ed_4yr +
low_bmi + ovwt_bmi + obese_bmi +
concep_spring + concep_summer + concep_fall +
concep_2010 + concep_2011 + concep_2012 + concep_2013 +
maternal_age + any_smoker + smokeSH +
mean_cpss + mean_epsd + male,
data = gam_df2, method = "REML")
summary(bw_gam2)##
## Family: gaussian
## Link function: identity
##
## Formula:
## birth_weight ~ s(mean_o3) + lat + lon + lat_lon_int + ed_no_hs +
## ed_hs + ed_aa + ed_4yr + low_bmi + ovwt_bmi + obese_bmi +
## concep_spring + concep_summer + concep_fall + concep_2010 +
## concep_2011 + concep_2012 + concep_2013 + maternal_age +
## any_smoker + smokeSH + mean_cpss + mean_epsd + male
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2764.480 479.111 5.770 0.0000000112 ***
## lat 1307.840 17720.490 0.074 0.94118
## lon -617.797 8343.493 -0.074 0.94099
## lat_lon_int 1590.626 21408.983 0.074 0.94079
## ed_no_hs 88.616 72.627 1.220 0.22276
## ed_hs 56.053 64.596 0.868 0.38579
## ed_aa 29.172 57.302 0.509 0.61083
## ed_4yr 56.889 50.524 1.126 0.26050
## low_bmi -142.276 91.396 -1.557 0.11993
## ovwt_bmi 52.214 39.867 1.310 0.19066
## obese_bmi 108.919 45.239 2.408 0.01627 *
## concep_spring -86.805 53.765 -1.615 0.10680
## concep_summer -22.561 79.126 -0.285 0.77561
## concep_fall 5.096 73.294 0.070 0.94459
## concep_2010 355.973 480.559 0.741 0.45906
## concep_2011 343.831 481.811 0.714 0.47566
## concep_2012 371.087 482.934 0.768 0.44247
## concep_2013 451.125 481.340 0.937 0.34892
## maternal_age 71.193 21.632 3.291 0.00104 **
## any_smoker -205.057 62.646 -3.273 0.00111 **
## smokeSH -65.480 43.764 -1.496 0.13499
## mean_cpss 25.661 19.688 1.303 0.19282
## mean_epsd -58.200 20.028 -2.906 0.00376 **
## male 141.871 32.270 4.396 0.0000124518 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(mean_o3) 3.841 4.785 4.648 0.000458 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.113 Deviance explained = 14.1%
## -REML = 6305.3 Scale est. = 2.166e+05 n = 851jpeg(here::here("Figs", "Ozone_GAM_Birth_Weight_Sensitivity_v4a.1.jpeg"))
plot(bw_gam2, main = "GAM with a smoothing term for ozone",
xlab = "Ozone (scaled)", ylab = "Change in birth weight (g)")
dev.off()## quartz_off_screen
## 28 GAM Sensitivity Analysis no. 2
Going to try the middle 90% of data as well, just in case
library(mgcv)
quantile(X.scaled[,"mean_o3"], probs = c(0.05, 0.95))## 5% 95%
## -1.568529 1.633168q_5 <- quantile(X.scaled[,"mean_o3"], probs = c(0.05))
q_95 <- quantile(X.scaled[,"mean_o3"], probs = c(0.95))
gam_df <- as.data.frame(cbind(Y, X.scaled[, "mean_o3"], W.scaled2))
names(gam_df)## [1] "birth_weight" "V2" "lat" "lon"
## [5] "lat_lon_int" "ed_no_hs" "ed_hs" "ed_aa"
## [9] "ed_4yr" "low_bmi" "ovwt_bmi" "obese_bmi"
## [13] "concep_spring" "concep_summer" "concep_fall" "concep_2010"
## [17] "concep_2011" "concep_2012" "concep_2013" "maternal_age"
## [21] "any_smoker" "smokeSH" "mean_cpss" "mean_epsd"
## [25] "male"names(gam_df)[2] <- "mean_o3"
head(gam_df)gam_df3 <- gam_df %>%
filter(mean_o3 > q_5 & mean_o3 < q_95)
hist(gam_df3$mean_o3)
bw_gam3 <- gam(birth_weight ~ s(mean_o3) +
lat + lon + lat_lon_int +
ed_no_hs + ed_hs + ed_aa + ed_4yr +
low_bmi + ovwt_bmi + obese_bmi +
concep_spring + concep_summer + concep_fall +
concep_2010 + concep_2011 + concep_2012 + concep_2013 +
maternal_age + any_smoker + smokeSH +
mean_cpss + mean_epsd + male,
data = gam_df3, method = "REML")
summary(bw_gam3)##
## Family: gaussian
## Link function: identity
##
## Formula:
## birth_weight ~ s(mean_o3) + lat + lon + lat_lon_int + ed_no_hs +
## ed_hs + ed_aa + ed_4yr + low_bmi + ovwt_bmi + obese_bmi +
## concep_spring + concep_summer + concep_fall + concep_2010 +
## concep_2011 + concep_2012 + concep_2013 + maternal_age +
## any_smoker + smokeSH + mean_cpss + mean_epsd + male
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2781.485 474.373 5.863 0.00000000669 ***
## lat 732.212 18067.795 0.041 0.967684
## lon -343.494 8506.550 -0.040 0.967801
## lat_lon_int 891.225 21828.164 0.041 0.967443
## ed_no_hs 93.180 73.374 1.270 0.204487
## ed_hs 56.855 65.381 0.870 0.384794
## ed_aa 42.347 58.286 0.727 0.467727
## ed_4yr 44.902 51.276 0.876 0.381469
## low_bmi -191.297 92.251 -2.074 0.038440 *
## ovwt_bmi 35.337 40.292 0.877 0.380747
## obese_bmi 96.066 46.273 2.076 0.038215 *
## concep_spring -101.146 54.478 -1.857 0.063739 .
## concep_summer -27.660 79.138 -0.350 0.726801
## concep_fall -9.852 73.236 -0.135 0.893022
## concep_2010 387.672 475.783 0.815 0.415431
## concep_2011 379.751 477.170 0.796 0.426368
## concep_2012 377.692 478.232 0.790 0.429904
## concep_2013 457.230 476.658 0.959 0.337735
## maternal_age 72.161 22.102 3.265 0.001143 **
## any_smoker -230.643 63.065 -3.657 0.000272 ***
## smokeSH -73.422 44.431 -1.652 0.098840 .
## mean_cpss 22.301 19.932 1.119 0.263556
## mean_epsd -55.958 20.318 -2.754 0.006022 **
## male 130.449 32.737 3.985 0.00007389872 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(mean_o3) 3.248 4.063 3.254 0.0116 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.112 Deviance explained = 14.1%
## -REML = 5962.4 Scale est. = 2.1182e+05 n = 807jpeg(here::here("Figs", "Ozone_GAM_Birth_Weight_Sensitivity_v4a.2.jpeg"))
plot(bw_gam3, main = "GAM with a smoothing term for ozone",
xlab = "Ozone (scaled)", ylab = "Change in birth weight (g)")
dev.off()## quartz_off_screen
## 2